[yorick-ygsl] 08/10: Reformat doc. and add global Emacs settings
Thibaut Jean-Claude Paumard
thibaut at moszumanska.debian.org
Thu Dec 1 13:27:10 UTC 2016
This is an automated email from the git hooks/post-receive script.
thibaut pushed a commit to branch upstream
in repository yorick-ygsl.
commit 30b0e22e1adadaa95777dc54b8fb845621862469
Author: Éric Thiébaut <eric.thiebaut at univ-lyon1.fr>
Date: Fri Mar 18 09:16:22 2016 +0100
Reformat doc. and add global Emacs settings
---
.dir-locals.el | 16 +
gsl.i | 1237 ++++++++++++++++++++++++++++----------------------------
ygsl.c | 14 +-
3 files changed, 629 insertions(+), 638 deletions(-)
diff --git a/.dir-locals.el b/.dir-locals.el
new file mode 100644
index 0000000..0628b21
--- /dev/null
+++ b/.dir-locals.el
@@ -0,0 +1,16 @@
+((nil . ((indent-tabs-mode . nil)
+ (tab-width . 8)
+ (coding . utf8)
+ (fill-column . 79)
+ (ispell-local-dictionary . "american")))
+ (c-mode . ((c-file-style . "bsd")
+ (c-basic-offset . 2)))
+ (java-mode . ((c-basic-offset . 4)))
+ (julia-mode . ())
+ (makefile-gmake-mode . ((indent-tabs-mode . t)))
+ (sh-mode . ((sh-basic-offset . 4)))
+ (tcl-mode . ((tcl-default-application . "wish")
+ (tcl-indent-level . 2)))
+ (yorick-mode . ((c-basic-offset . 2)
+ (fill-column . 78)))
+)
diff --git a/gsl.i b/gsl.i
index 7f48062..c756f1c 100644
--- a/gsl.i
+++ b/gsl.i
@@ -5,7 +5,7 @@
*
*-----------------------------------------------------------------------------
*
- * Copyright (C) 2012 Éric Thiébaut <eric.thiebaut at univ-lyon1.fr>
+ * Copyright (C) 2012-2016 Éric Thiébaut <eric.thiebaut at univ-lyon1.fr>
*
* This software is governed by the CeCILL-C license under French law and
* abiding by the rules of distribution of free software. You can use, modify
@@ -39,37 +39,37 @@ if (is_func(plug_in)) plug_in, "ygsl";
local gsl_sf;
/* DOCUMENT gsl_sf_*
- *
- * Special functions from GSL (GNU Scientific Library) are prefixed with
- * "gsl_sf_"; to obtain more information, see the following documentation
- * entries:
- *
- * gsl_sf_airy_Ai - Airy functions
- * gsl_sf_bessel_J0 - regular cylindrical Bessel functions
- * gsl_sf_bessel_Y0 - irregular cylindrical Bessel functions
- * gsl_sf_bessel_I0 - regular modified cylindrical Bessel functions
- * gsl_sf_bessel_K0 - irregular modified cylindrical Bessel functions
- * gsl_sf_bessel_j0 - regular spherical Bessel functions
- * gsl_sf_bessel_y0 - irregular spherical Bessel functions
- * gsl_sf_bessel_i0_scaled - regular modified spherical Bessel functions
- * gsl_sf_bessel_k0_scaled - irregular modified spherical Bessel functions
- * gsl_sf_clausen - Clausen function
- * gsl_sf_dawson - Dawson integral
- * gsl_sf_debye - Debye functions
- * gsl_sf_dilog - dilogarithm
- * gsl_sf_ellint_Kcomp - Legendre form of complete elliptic integrals
- * gsl_sf_erf - error functions
- * gsl_sf_exp - exponential and logarithm functions
- * gsl_sf_expint - exponential, hyperbolic and trigonometric integrals
- * gsl_sf_fermi_dirac - Fermi-Dirac integrals
- * gsl_sf_gamma - Gamma functions
- * gsl_sf_psi - Digamma, trigamma and polygamma functions
- * gsl_sf_lamber - Lambert's functions
- * gsl_sf_legendre - Legendre polynomials
- * gsl_sf_synchrotron - synchrotron functions
- * gsl_sf_transport - transport functions
- * gsl_sf_sin - trigonometric functions
- * gsl_sf_zeta - Zeta functions
+
+ Special functions from GSL (GNU Scientific Library) are prefixed with
+ "gsl_sf_"; to obtain more information, see the following documentation
+ entries:
+
+ gsl_sf_airy_Ai - Airy functions
+ gsl_sf_bessel_J0 - regular cylindrical Bessel functions
+ gsl_sf_bessel_Y0 - irregular cylindrical Bessel functions
+ gsl_sf_bessel_I0 - regular modified cylindrical Bessel functions
+ gsl_sf_bessel_K0 - irregular modified cylindrical Bessel functions
+ gsl_sf_bessel_j0 - regular spherical Bessel functions
+ gsl_sf_bessel_y0 - irregular spherical Bessel functions
+ gsl_sf_bessel_i0_scaled - regular modified spherical Bessel functions
+ gsl_sf_bessel_k0_scaled - irregular modified spherical Bessel functions
+ gsl_sf_clausen - Clausen function
+ gsl_sf_dawson - Dawson integral
+ gsl_sf_debye - Debye functions
+ gsl_sf_dilog - dilogarithm
+ gsl_sf_ellint_Kcomp - Legendre form of complete elliptic integrals
+ gsl_sf_erf - error functions
+ gsl_sf_exp - exponential and logarithm functions
+ gsl_sf_expint - exponential, hyperbolic and trigonometric integrals
+ gsl_sf_fermi_dirac - Fermi-Dirac integrals
+ gsl_sf_gamma - Gamma functions
+ gsl_sf_psi - Digamma, trigamma and polygamma functions
+ gsl_sf_lamber - Lambert's functions
+ gsl_sf_legendre - Legendre polynomials
+ gsl_sf_synchrotron - synchrotron functions
+ gsl_sf_transport - transport functions
+ gsl_sf_sin - trigonometric functions
+ gsl_sf_zeta - Zeta functions
*/
extern gsl_sf_airy_Ai;
@@ -81,65 +81,64 @@ extern gsl_sf_airy_Bi_deriv;
extern gsl_sf_airy_Ai_deriv_scaled;
extern gsl_sf_airy_Bi_deriv_scaled;
/* DOCUMENT gsl_sf_airy_Ai(x [,flags])
- * gsl_sf_airy_Bi(x [,flags])
- * gsl_sf_airy_Ai_deriv(x [,flags])
- * gsl_sf_airy_Bi_deriv(x [,flags])
- * gsl_sf_airy_Ai_scaled(x [,flags])
- * gsl_sf_airy_Bi_scaled(x [,flags])
- * gsl_sf_airy_Ai_deriv_scaled(x [,flags])
- * gsl_sf_airy_Bi_deriv_scaled(x [,flags])
- *
- * These routines compute the Airy functions and derivatives for the
- * argument X (a non-complex numerical array).
- *
- * The routines gsl_sf_airy_Ai and gsl_sf_airy_Bi compute Airy functions
- * Ai(x) and Bi(x) which are defined by the integral representations:
- *
- * Ai(x) = (1/PI) \int_0^\infty cos((1/3)*t^3 + x*t) dt
- * Bi(x) = (1/PI) \int_0^\infty (exp(-(1/3)*t^3)
- * + sin((1/3)*t^3 + x*t)) dt
- *
- * The routines gsl_sf_airy_Ai_deriv and gsl_sf_airy_Bi_deriv compute
- * the derivatives of the Airy functions.
- *
- * The routines gsl_sf_airy_Ai_scaled and gsl_sf_airy_Bi_scaled compute
- * a scaled version of the Airy functions S_A(x) Ai(x) and S_B(x) Bi(x).
- * The scaling factors are:
- * S_A(x) = exp(+(2/3)*x^(3/2)), for x>0
- * 1, for x<0;
- * S_B(x) = exp(-(2/3)*x^(3/2)), for x>0
- * 1, for x<0.
- *
- * The routines gsl_sf_airy_Ai_deriv_scaled and
- * gsl_sf_airy_Bi_deriv_scaled compute the derivatives of the scaled Airy
- * functions.
- *
- * The optional FLAGS argument is a bitwise combination which specifies
- * the relative accuracy of the result and if an estimate of the error
- * is required:
- *
- * (FLAGS & 1) is non-zero to compute an estimate of the error, the
- * result, says Y, has an additional dimension of length 2
- * prepended to the dimension list of X:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- * (FLAGS & 6) is the accuracy mode:
- * 6 - Double-precision (GSL_PREC_DOUBLE), a relative accuracy of
- * approximately 2e-16.
- * 4 - Single-precision (GSL_PREC_SINGLE), a relative accuracy of
- * approximately 1e-7.
- * 2 - Approximate values (GSL_PREC_APPROX), a relative accuracy
- * of approximately 5e-4.
- * 0 - Default accuracy (GSL_PREC_DOUBLE).
- *
- * For instance, with FLAGS=1, function values are computed with relative
- * accuracy of 2e-16 and an estimate of the error is returned; with
- * FLAGS=2, approximate values with relative accuracy of 5e-4 are
- * returned without error estimate
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_airy_Bi(x [,flags])
+ gsl_sf_airy_Ai_deriv(x [,flags])
+ gsl_sf_airy_Bi_deriv(x [,flags])
+ gsl_sf_airy_Ai_scaled(x [,flags])
+ gsl_sf_airy_Bi_scaled(x [,flags])
+ gsl_sf_airy_Ai_deriv_scaled(x [,flags])
+ gsl_sf_airy_Bi_deriv_scaled(x [,flags])
+
+ These routines compute the Airy functions and derivatives for the
+ argument X (a non-complex numerical array).
+
+ The routines gsl_sf_airy_Ai and gsl_sf_airy_Bi compute Airy functions
+ Ai(x) and Bi(x) which are defined by the integral representations:
+
+ Ai(x) = (1/PI) \int_0^\infty cos((1/3)*t^3 + x*t) dt
+ Bi(x) = (1/PI) \int_0^\infty (exp(-(1/3)*t^3)
+ + sin((1/3)*t^3 + x*t)) dt
+
+ The routines gsl_sf_airy_Ai_deriv and gsl_sf_airy_Bi_deriv compute the
+ derivatives of the Airy functions.
+
+ The routines gsl_sf_airy_Ai_scaled and gsl_sf_airy_Bi_scaled compute
+ a scaled version of the Airy functions S_A(x) Ai(x) and S_B(x) Bi(x).
+ The scaling factors are:
+ S_A(x) = exp(+(2/3)*x^(3/2)), for x>0
+ 1, for x<0;
+ S_B(x) = exp(-(2/3)*x^(3/2)), for x>0
+ 1, for x<0.
+
+ The routines gsl_sf_airy_Ai_deriv_scaled and gsl_sf_airy_Bi_deriv_scaled
+ compute the derivatives of the scaled Airy functions.
+
+ The optional FLAGS argument is a bitwise combination which specifies the
+ relative accuracy of the result and if an estimate of the error is
+ required:
+
+ (FLAGS & 1) is non-zero to compute an estimate of the error, the
+ result, says Y, has an additional dimension of length 2 prepended
+ to the dimension list of X:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+ (FLAGS & 6) is the accuracy mode:
+ 6 - Double-precision (GSL_PREC_DOUBLE), a relative accuracy of
+ approximately 2e-16.
+ 4 - Single-precision (GSL_PREC_SINGLE), a relative accuracy of
+ approximately 1e-7.
+ 2 - Approximate values (GSL_PREC_APPROX), a relative accuracy
+ of approximately 5e-4.
+ 0 - Default accuracy (GSL_PREC_DOUBLE).
+
+ For instance, with FLAGS=1, function values are computed with relative
+ accuracy of 2e-16 and an estimate of the error is returned; with FLAGS=2,
+ approximate values with relative accuracy of 5e-4 are returned without
+ error estimate
+
+
+ SEE ALSO: gsl_sf.
*/
extern gsl_sf_bessel_J0;
@@ -147,26 +146,25 @@ extern gsl_sf_bessel_J1;
extern gsl_sf_bessel_Jn;
extern gsl_sf_bessel_Jnu;
/* DOCUMENT gsl_sf_bessel_J0(x [,err])
- * gsl_sf_bessel_J1(x [,err])
- * gsl_sf_bessel_Jn(n, x [,err])
- * gsl_sf_bessel_Jnu(nu, x [,err])
- *
- * These functions compute the regular cylindrical Bessel functions for
- * argument X (a non-complex numerical array or scalar) and of various
- * order: zeroth order, J_0(x); first order, J_1(x), integer order order
- * N, J_n(x), and fractional order NU, J_nu(x). N must be a scalar
- * integer and NU a scalar real.
- *
- * If optional argument ERR is true, these functions also compute an
- * estimate of the error, the result, says Y, has an additional dimension
- * of length 2 prepended to the dimension list of X:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_Y0, gsl_sf_bessel_I0, gsl_sf_bessel_K0,
- * gsl_sf_bessel_j0, gsl_sf_bessel_y0, gsl_sf_bessel_i0,
- * gsl_sf_bessel_k0.
+ gsl_sf_bessel_J1(x [,err])
+ gsl_sf_bessel_Jn(n, x [,err])
+ gsl_sf_bessel_Jnu(nu, x [,err])
+
+ These functions compute the regular cylindrical Bessel functions for
+ argument X (a non-complex numerical array or scalar) and of various
+ order: zeroth order, J_0(x); first order, J_1(x), integer order order N,
+ J_n(x), and fractional order NU, J_nu(x). N must be a scalar integer and
+ NU a scalar real.
+
+ If optional argument ERR is true, these functions also compute an
+ estimate of the error, the result, says Y, has an additional dimension of
+ length 2 prepended to the dimension list of X: Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_Y0, gsl_sf_bessel_I0, gsl_sf_bessel_K0,
+ gsl_sf_bessel_j0, gsl_sf_bessel_y0, gsl_sf_bessel_i0,
+ gsl_sf_bessel_k0.
*/
extern gsl_sf_bessel_Y0;
@@ -174,16 +172,16 @@ extern gsl_sf_bessel_Y1;
extern gsl_sf_bessel_Yn;
extern gsl_sf_bessel_Ynu;
/* DOCUMENT gsl_sf_bessel_Y0(x [,err])
- * gsl_sf_bessel_Y1(x [,err])
- * gsl_sf_bessel_Yn(n, x [,err])
- * gsl_sf_bessel_Ynu(nu, x [,err])
- *
- * These functions compute the irregular cylindrical Bessel functions for
- * X>0. See gsl_sf_bessel_J0 for a more detailled description of the
- * arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_Y1(x [,err])
+ gsl_sf_bessel_Yn(n, x [,err])
+ gsl_sf_bessel_Ynu(nu, x [,err])
+
+ These functions compute the irregular cylindrical Bessel functions for
+ X>0. See gsl_sf_bessel_J0 for a more detailled description of the
+ arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_I0;
@@ -195,21 +193,21 @@ extern gsl_sf_bessel_I1_scaled;
extern gsl_sf_bessel_In_scaled;
extern gsl_sf_bessel_Inu_scaled;
/* DOCUMENT gsl_sf_bessel_I0(x [,err])
- * gsl_sf_bessel_I1(x [,err])
- * gsl_sf_bessel_In(n, x [,err])
- * gsl_sf_bessel_Inu(nu, x [,err])
- * gsl_sf_bessel_I0_scaled(x [,err])
- * gsl_sf_bessel_I1_scaled(x [,err])
- * gsl_sf_bessel_In_scaled(n, x [,err])
- * gsl_sf_bessel_Inu_scaled(nu, x [,err])
- *
- * These routines compute the regular modified cylindrical Bessel
- * functions and their scaled counterparts. The scaling factor is
- * exp(-abs(X)); for instance: I0_scaled(X) = exp(-abs(X))*I0(X). See
- * gsl_sf_bessel_J0 for a more detailled description of the arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_I1(x [,err])
+ gsl_sf_bessel_In(n, x [,err])
+ gsl_sf_bessel_Inu(nu, x [,err])
+ gsl_sf_bessel_I0_scaled(x [,err])
+ gsl_sf_bessel_I1_scaled(x [,err])
+ gsl_sf_bessel_In_scaled(n, x [,err])
+ gsl_sf_bessel_Inu_scaled(nu, x [,err])
+
+ These routines compute the regular modified cylindrical Bessel functions
+ and their scaled counterparts. The scaling factor is exp(-abs(X)); for
+ instance: I0_scaled(X) = exp(-abs(X))*I0(X). See gsl_sf_bessel_J0 for a
+ more detailled description of the arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_K0;
@@ -222,24 +220,24 @@ extern gsl_sf_bessel_K1_scaled;
extern gsl_sf_bessel_Kn_scaled;
extern gsl_sf_bessel_Knu_scaled;
/* DOCUMENT gsl_sf_bessel_K0(x [,err])
- * gsl_sf_bessel_K1(x [,err])
- * gsl_sf_bessel_Kn(n, x [,err])
- * gsl_sf_bessel_Knu(nu, x [,err])
- * gsl_sf_bessel_lnKnu(nu, x [,err])
- * gsl_sf_bessel_K0_scaled(x [,err])
- * gsl_sf_bessel_K1_scaled(x [,err])
- * gsl_sf_bessel_Kn_scaled(n, x [,err])
- * gsl_sf_bessel_Knu_scaled(nu, x [,err])
- *
- * These routines compute the irregular modified cylindrical Bessel
- * functions and their scaled counterparts. The scaling factor is exp(X)
- * for X>0; for instance: K0_scaled(X) = exp(X)*K0(X). The function
- * gsl_sf_bessel_lnKnu computes the logarithm of the irregular modified
- * Bessel function of fractional order NU. See gsl_sf_bessel_J0 for a
- * more detailled description of the arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_K1(x [,err])
+ gsl_sf_bessel_Kn(n, x [,err])
+ gsl_sf_bessel_Knu(nu, x [,err])
+ gsl_sf_bessel_lnKnu(nu, x [,err])
+ gsl_sf_bessel_K0_scaled(x [,err])
+ gsl_sf_bessel_K1_scaled(x [,err])
+ gsl_sf_bessel_Kn_scaled(n, x [,err])
+ gsl_sf_bessel_Knu_scaled(nu, x [,err])
+
+ These routines compute the irregular modified cylindrical Bessel
+ functions and their scaled counterparts. The scaling factor is exp(X)
+ for X>0; for instance: K0_scaled(X) = exp(X)*K0(X). The function
+ gsl_sf_bessel_lnKnu computes the logarithm of the irregular modified
+ Bessel function of fractional order NU. See gsl_sf_bessel_J0 for a more
+ detailled description of the arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_j0;
@@ -247,17 +245,17 @@ extern gsl_sf_bessel_j1;
extern gsl_sf_bessel_j2;
extern gsl_sf_bessel_jl;
/* DOCUMENT gsl_sf_bessel_j0(x [,err])
- * gsl_sf_bessel_j1(x [,err])
- * gsl_sf_bessel_j2(x [,err])
- * gsl_sf_bessel_jl(l, x [,err])
- *
- * These routines compute the regular spherical Bessel functions of
- * zeroth order (j0), first order (j1), second order (j2) and l-th order
- * (jl, for X>=0 and L>=0). See gsl_sf_bessel_J0 for a more detailled
- * description of the arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_j1(x [,err])
+ gsl_sf_bessel_j2(x [,err])
+ gsl_sf_bessel_jl(l, x [,err])
+
+ These routines compute the regular spherical Bessel functions of zeroth
+ order (j0), first order (j1), second order (j2) and l-th order (jl, for
+ X>=0 and L>=0). See gsl_sf_bessel_J0 for a more detailled description of
+ the arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_y0;
@@ -265,23 +263,22 @@ extern gsl_sf_bessel_y1;
extern gsl_sf_bessel_y2;
extern gsl_sf_bessel_yl;
/* DOCUMENT gsl_sf_bessel_y0(x [,err])
- * gsl_sf_bessel_y1(x [,err])
- * gsl_sf_bessel_y2(x [,err])
- * gsl_sf_bessel_yl(l, x [,err])
- *
- * These routines compute the irregular spherical Bessel functions of
- * zeroth order (y0), first order (y1), second order (y2) and l-th order
- * (yl, for L>=0):
- *
- * y0(x) = -cos(x)/x
- * y1(x) = -(cos(x)/x + sin(x))/x
- * y2(x) = (-3/x^3 + 1/x)*cos(x) - (3/x^2)*sin(x)
- *
- * See gsl_sf_bessel_J0 for a more detailled description of the
- * arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_y1(x [,err])
+ gsl_sf_bessel_y2(x [,err])
+ gsl_sf_bessel_yl(l, x [,err])
+
+ These routines compute the irregular spherical Bessel functions of zeroth
+ order (y0), first order (y1), second order (y2) and l-th order (yl, for
+ L>=0):
+
+ y0(x) = -cos(x)/x
+ y1(x) = -(cos(x)/x + sin(x))/x
+ y2(x) = (-3/x^3 + 1/x)*cos(x) - (3/x^2)*sin(x)
+
+ See gsl_sf_bessel_J0 for a more detailled description of the arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_i0_scaled;
@@ -289,26 +286,25 @@ extern gsl_sf_bessel_i1_scaled;
extern gsl_sf_bessel_i2_scaled;
extern gsl_sf_bessel_il_scaled;
/* DOCUMENT gsl_sf_bessel_i0_scaled(x [,err])
- * gsl_sf_bessel_i1_scaled(x [,err])
- * gsl_sf_bessel_i2_scaled(x [,err])
- * gsl_sf_bessel_il_scaled(l, x [,err])
- *
- * These routines compute the regular modified spherical Bessel functions
- * of zeroth order (i0), first order (i1), second order (i2) and l-th
- * order (il):
- *
- * il_scaled(x) = exp(-abs(x))*il(x)
- *
- * The regular modified spherical Bessel functions i_l(x) are related to
- * the modified Bessel functions of fractional order by:
- *
- * i_l(x) = sqrt(PI/(2*x))*I_{l + 1/2}(x)
- *
- * See gsl_sf_bessel_J0 for a more detailled description of the
- * arguments.
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_i1_scaled(x [,err])
+ gsl_sf_bessel_i2_scaled(x [,err])
+ gsl_sf_bessel_il_scaled(l, x [,err])
+
+ These routines compute the regular modified spherical Bessel functions of
+ zeroth order (i0), first order (i1), second order (i2) and l-th order
+ (il):
+
+ il_scaled(x) = exp(-abs(x))*il(x)
+
+ The regular modified spherical Bessel functions i_l(x) are related to the
+ modified Bessel functions of fractional order by:
+
+ i_l(x) = sqrt(PI/(2*x))*I_{l + 1/2}(x)
+
+ See gsl_sf_bessel_J0 for a more detailled description of the arguments.
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_bessel_k0_scaled;
@@ -316,61 +312,61 @@ extern gsl_sf_bessel_k1_scaled;
extern gsl_sf_bessel_k2_scaled;
extern gsl_sf_bessel_kl_scaled;
/* DOCUMENT gsl_sf_bessel_k0_scaled(x [,err])
- * gsl_sf_bessel_k1_scaled(x [,err])
- * gsl_sf_bessel_k2_scaled(x [,err])
- * gsl_sf_bessel_kl_scaled(l, x [,err])
- *
- * These routines compute the irregular modified spherical Bessel
- * functions of zeroth order (k0), first order (k1), second order (k2)
- * and l-th order (kl), for X>0:
- *
- * kl_scaled(x) = exp(x)*kl(x)
- *
- * The irregular modified spherical Bessel functions i_l(x) are related to
- * the modified Bessel functions of fractional order by:
- *
- * k_l(x) = sqrt(PI/(2*x))*K_{l + 1/2}(x)
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
+ gsl_sf_bessel_k1_scaled(x [,err])
+ gsl_sf_bessel_k2_scaled(x [,err])
+ gsl_sf_bessel_kl_scaled(l, x [,err])
+
+ These routines compute the irregular modified spherical Bessel functions
+ of zeroth order (k0), first order (k1), second order (k2) and l-th order
+ (kl), for X>0:
+
+ kl_scaled(x) = exp(x)*kl(x)
+
+ The irregular modified spherical Bessel functions i_l(x) are related to
+ the modified Bessel functions of fractional order by:
+
+ k_l(x) = sqrt(PI/(2*x))*K_{l + 1/2}(x)
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf, gsl_sf_bessel_J0.
*/
extern gsl_sf_clausen;
/* DOCUMENT gsl_sf_clausen(x [,err])
- *
- * Returns the Clausen function Cl_2 of its argument X.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+
+ Returns the Clausen function Cl_2 of its argument X.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
extern gsl_sf_dawson;
/* DOCUMENT gsl_sf_dawson(x [,err])
- *
- * Returns the Dawson integral of its argument X defined by:
- *
- * exp(-x^2) \int_0^x exp(t^2) dt
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+
+ Returns the Dawson integral of its argument X defined by:
+
+ exp(-x^2) \int_0^x exp(t^2) dt
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
extern gsl_sf_debye_1;
@@ -381,49 +377,50 @@ extern gsl_sf_debye_5;
extern gsl_sf_debye_6;
local gsl_sf_debye;
/* DOCUMENT gsl_sf_debye_1(x [,err])
- * gsl_sf_debye_2(x [,err])
- * gsl_sf_debye_3(x [,err])
- * gsl_sf_debye_4(x [,err])
- * gsl_sf_debye_5(x [,err])
- * gsl_sf_debye_6(x [,err])
- *
- * Return the Debye function D_n(x) of argument X defined by the
- * following integral:
- *
- * D_n(x) = n/x^n \int_0^x (t^n/(e^t - 1)) dt
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+ gsl_sf_debye_2(x [,err])
+ gsl_sf_debye_3(x [,err])
+ gsl_sf_debye_4(x [,err])
+ gsl_sf_debye_5(x [,err])
+ gsl_sf_debye_6(x [,err])
+
+ Return the Debye function D_n(x) of argument X defined by the following
+ integral:
+
+ D_n(x) = n/x^n \int_0^x (t^n/(e^t - 1)) dt
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
extern gsl_sf_dilog;
/* DOCUMENT gsl_sf_dilog(x [,err])
- *
- * Return the dilogarithm for a real argument X. If optional argument
- * ERR is true, the result, says Y, has an additional dimension of length
- * 2 prepended to the dimension list of X which is used to provide an
- * estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+
+ Return the dilogarithm for a real argument X. If optional argument ERR
+ is true, the result, says Y, has an additional dimension of length 2
+ prepended to the dimension list of X which is used to provide an estimate
+ of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
extern gsl_sf_ellint_Kcomp;
extern gsl_sf_ellint_Ecomp;
/* DOCUMENT gsl_sf_ellint_Kcomp(k [,flags])
- * gsl_sf_ellint_Ecomp(k [,flags])
- * Return the complete elliptic integral K(k) or E(k). See
- * gsl_sf_airy_Ai for the meaning of optional argument FLAGS.
- *
- * SEE ALSO: gsl_sf, gsl_sf_airy_Ai.
+ gsl_sf_ellint_Ecomp(k [,flags])
+
+ Return the complete elliptic integral K(k) or E(k). See gsl_sf_airy_Ai
+ for the meaning of optional argument FLAGS.
+
+ SEE ALSO: gsl_sf, gsl_sf_airy_Ai.
*/
extern gsl_sf_erf;
@@ -433,46 +430,47 @@ extern gsl_sf_erf_Z;
extern gsl_sf_erf_Q;
extern gsl_sf_hazard;
/* DOCUMENT gsl_sf_erf(x [,err])
- * gsl_sf_erfc(x [,err])
- * gsl_sf_log_erfc(x [,err])
- * gsl_sf_erf_Q(x [,err])
- * gsl_sf_erf_Z(x [,err])
- * gsl_sf_hazard(x [,err])
- *
- * gsl_sf_erf(x) computes the error function:
- *
- * erf(x) = (2/sqrt(pi)) \int_0^x exp(-t^2) dt
- *
- * gsl_sf_erfc(x) computes the complementary error function:
- *
- * erfc(x) = 1 - erf(x)
- * = (2/sqrt(pi)) \int_x^\infty exp(-t^2) dt
- *
- * gsl_sf_log_erfc(x) computes the logarithm of the complementary error function.
- *
- * gsl_sf_erf_Z(x) computes the Gaussian probability density function:
- *
- * Z(x) = (1/sqrt(2 pi)) \exp(-x^2/2).
- *
- * gsl_sf_erf_Q(x) computes the upper tail of the Gaussian probability
- * density function:
- *
- * Q(x) = (1/sqrt(2 pi)) \int_x^\infty \exp(-t^2/2) dt.
- *
- * gsl_sf_hazard(x) computes the hazard function for the normal
- * distribution, also known as the inverse Mill's ratio:
- *
- * h(x) = Z(x)/Q(x)
- * = sqrt(2/pi) exp(-x^2/2)/erfc(x/sqrt(2)).
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+ gsl_sf_erfc(x [,err])
+ gsl_sf_log_erfc(x [,err])
+ gsl_sf_erf_Q(x [,err])
+ gsl_sf_erf_Z(x [,err])
+ gsl_sf_hazard(x [,err])
+
+ gsl_sf_erf(x) computes the error function:
+
+ erf(x) = (2/sqrt(pi)) \int_0^x exp(-t^2) dt
+
+ gsl_sf_erfc(x) computes the complementary error function:
+
+ erfc(x) = 1 - erf(x)
+ = (2/sqrt(pi)) \int_x^\infty exp(-t^2) dt
+
+ gsl_sf_log_erfc(x) computes the logarithm of the complementary error
+ function.
+
+ gsl_sf_erf_Z(x) computes the Gaussian probability density function:
+
+ Z(x) = (1/sqrt(2 pi)) \exp(-x^2/2).
+
+ gsl_sf_erf_Q(x) computes the upper tail of the Gaussian probability
+ density function:
+
+ Q(x) = (1/sqrt(2 pi)) \int_x^\infty \exp(-t^2/2) dt.
+
+ gsl_sf_hazard(x) computes the hazard function for the normal
+ distribution, also known as the inverse Mill's ratio:
+
+ h(x) = Z(x)/Q(x)
+ = sqrt(2/pi) exp(-x^2/2)/erfc(x/sqrt(2)).
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
extern gsl_sf_exp;
@@ -485,55 +483,54 @@ extern gsl_sf_log_abs;
extern gsl_sf_log_1plusx;
extern gsl_sf_log_1plusx_mx;
/* DOCUMENT gsl_sf_exp(x [,err])
- * gsl_sf_expm1(x [,err])
- * gsl_sf_exprel(x [,err])
- * gsl_sf_exprel_2(x [,err])
- * gsl_sf_exprel_n(n, x [,err])
- * gsl_sf_log(x [,err])
- * gsl_sf_log_abs(x [,err])
- * gsl_sf_log_1plusx(x [,err])
- * gsl_sf_log_1plusx_mx(x [,err])
- *
- * gsl_sf_exp(X) computes the exponential of X.
- *
- * gsl_sf_expm1(X) computes the quantity exp(X) - 1 using an algorithm
- * that is accurate for small X.
- *
- * gsl_sf_exprel(X) computes the quantity (exp(X) - 1)/X using an
- * algorithm that is accurate for small X and which is based on the
- * expansion:
- *
- * (exp(x) - 1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + ...
- *
- * gsl_sf_exprel_2(X) computes the quantity 2*(exp(X) - 1)/X^2 using an
- * algorithm that is accurate for small X and which is based on the
- * expansion:
- *
- * 2*(exp(x) - 1 - x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + ...
- *
- * gsl_sf_exprel_n(N,X) computes the N-relative exponential (N must be a
- * scalar integer):
- *
- * expre_n(x) = n! / x^n ( exp(x) - \sum_{k=0}^{n-1} x^k / k! )
- *
- * gsl_sf_log(X) computes the logarithm of X, for X > 0.
- *
- * gsl_sf_log_abs(X) computes the logarithm of |X|, for X != 0.
- *
- * gsl_sf_log_1plusx(x) computes log(1 + X) for X > -1 using an algorithm
- * that is accurate for small X.
- *
- * gsl_sf_log_1plusx_mx(x) computes log(1 + X) - X for X > -1 using an
- * algorithm that is accurate for small X.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+ gsl_sf_expm1(x [,err])
+ gsl_sf_exprel(x [,err])
+ gsl_sf_exprel_2(x [,err])
+ gsl_sf_exprel_n(n, x [,err])
+ gsl_sf_log(x [,err])
+ gsl_sf_log_abs(x [,err])
+ gsl_sf_log_1plusx(x [,err])
+ gsl_sf_log_1plusx_mx(x [,err])
+
+ gsl_sf_exp(X) computes the exponential of X.
+
+ gsl_sf_expm1(X) computes the quantity exp(X) - 1 using an algorithm that
+ is accurate for small X.
+
+ gsl_sf_exprel(X) computes the quantity (exp(X) - 1)/X using an algorithm
+ that is accurate for small X and which is based on the expansion:
+
+ (exp(x) - 1)/x = 1 + x/2 + x^2/(2*3) + x^3/(2*3*4) + ...
+
+ gsl_sf_exprel_2(X) computes the quantity 2*(exp(X) - 1)/X^2 using an
+ algorithm that is accurate for small X and which is based on the
+ expansion:
+
+ 2*(exp(x) - 1 - x)/x^2 = 1 + x/3 + x^2/(3*4) + x^3/(3*4*5) + ...
+
+ gsl_sf_exprel_n(N,X) computes the N-relative exponential (N must be a
+ scalar integer):
+
+ expre_n(x) = n! / x^n ( exp(x) - \sum_{k=0}^{n-1} x^k / k! )
+
+ gsl_sf_log(X) computes the logarithm of X, for X > 0.
+
+ gsl_sf_log_abs(X) computes the logarithm of |X|, for X != 0.
+
+ gsl_sf_log_1plusx(x) computes log(1 + X) for X > -1 using an algorithm
+ that is accurate for small X.
+
+ gsl_sf_log_1plusx_mx(x) computes log(1 + X) - X for X > -1 using an
+ algorithm that is accurate for small X.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
local gsl_sf_expint;
@@ -547,52 +544,52 @@ extern gsl_sf_Si;
extern gsl_sf_Ci;
extern gsl_sf_atanint;
/* DOCUMENT gsl_sf_expint_E1(x [, err])
- * gsl_sf_expint_E2(x [, err])
- * gsl_sf_expint_Ei(x [, err])
- * gsl_sf_expint_3(x [, err])
- * gsl_sf_Shi(x [, err])
- * gsl_sf_Chi(x [, err])
- * gsl_sf_Si(x [, err])
- * gsl_sf_Ci(x [, err])
- * gsl_sf_atanint(x [, err])
- *
- * gsl_sf_expint_E1(X) computes the exponential integral:
- * E1(x) = \int_1^\infty exp(-x t)/t dt
- *
- * gsl_sf_expint_E2(X) computes the second-order exponential integral:
- * E2(x) = \int_1^\infty exp(-x t)/t^2 dt
- *
- * gsl_sf_expint_E2(X) computes the exponetial integral:
- * Ei(x) = -PV( \int_{-x}^\infty exp(-t)/t dt )
- * where PV() denotes the principal value.
- *
- * gsl_sf_expint_3(X) computes the third-order exponential integral:
- * Ei_3(x) = \int_0^x \exp(-t^3) dt for x >= 0.
- *
- * gsl_sf_Shi(X) computes the integral:
- * Shi(x) = \int_0^x sinh(t)/t dt.
- *
- * gsl_sf_Chi(X) computes the integral:
- * Chi(x) = Re[ gamma_E + log(x) + \int_0^x (cosh(t) - 1)/t dt ]
- * where gamma_E is the Euler constant.
- *
- * gsl_sf_Si(X) computes the Sine integral:
- * Si(x) = \int_0^x sin(t)/t dt.
- *
- * gsl_sf_Ci(X) computes the Cosine integral:
- * Ci(x) = -\int_x^\int_x cos(t)/t dt for x > 0.
- *
- * gsl_sf_atanint(X) computes the arc-tangent integral:
- * AtanInt(x) = \int_0^x arctan(t)/t dt.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf
+ gsl_sf_expint_E2(x [, err])
+ gsl_sf_expint_Ei(x [, err])
+ gsl_sf_expint_3(x [, err])
+ gsl_sf_Shi(x [, err])
+ gsl_sf_Chi(x [, err])
+ gsl_sf_Si(x [, err])
+ gsl_sf_Ci(x [, err])
+ gsl_sf_atanint(x [, err])
+
+ gsl_sf_expint_E1(X) computes the exponential integral:
+ E1(x) = \int_1^\infty exp(-x t)/t dt
+
+ gsl_sf_expint_E2(X) computes the second-order exponential integral:
+ E2(x) = \int_1^\infty exp(-x t)/t^2 dt
+
+ gsl_sf_expint_E2(X) computes the exponetial integral:
+ Ei(x) = -PV( \int_{-x}^\infty exp(-t)/t dt )
+ where PV() denotes the principal value.
+
+ gsl_sf_expint_3(X) computes the third-order exponential integral:
+ Ei_3(x) = \int_0^x \exp(-t^3) dt for x >= 0.
+
+ gsl_sf_Shi(X) computes the integral:
+ Shi(x) = \int_0^x sinh(t)/t dt.
+
+ gsl_sf_Chi(X) computes the integral:
+ Chi(x) = Re[ gamma_E + log(x) + \int_0^x (cosh(t) - 1)/t dt ]
+ where gamma_E is the Euler constant.
+
+ gsl_sf_Si(X) computes the Sine integral:
+ Si(x) = \int_0^x sin(t)/t dt.
+
+ gsl_sf_Ci(X) computes the Cosine integral:
+ Ci(x) = -\int_x^\int_x cos(t)/t dt for x > 0.
+
+ gsl_sf_atanint(X) computes the arc-tangent integral:
+ AtanInt(x) = \int_0^x arctan(t)/t dt.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf
*/
local gsl_sf_fermi_dirac;
@@ -605,54 +602,54 @@ extern gsl_sf_fermi_dirac_half;
extern gsl_sf_fermi_dirac_3half;
extern gsl_sf_fermi_dirac_int;
/* DOCUMENT gsl_sf_fermi_dirac_int(j, x [, err])
- * gsl_sf_fermi_dirac_m1(x [, err])
- * gsl_sf_fermi_dirac_0(x [, err])
- * gsl_sf_fermi_dirac_1(x [, err])
- * gsl_sf_fermi_dirac_2(x [, err])
- * gsl_sf_fermi_dirac_mhalf(x [, err])
- * gsl_sf_fermi_dirac_half(x [, err])
- * gsl_sf_fermi_dirac_3half(x [, err])
- *
- * gsl_sf_fermi_dirac_int(J,X) computes the complete Fermi-Dirac integral
- * with an index of J:
- * F_j(x) = 1/Gamma(j + 1) \int_0^\infty t^j/(exp(t - x) + 1) dt
- * where J is a scalar integer and Gamma() is the Gamma function:
- * Gamma(n) = (n - 1)!
- * for integer n.
- *
- * gsl_sf_fermi_dirac_m1(X) computes the complete Fermi-Dirac integral
- * with an index of -1:
- * F_{-1}(x) = exp(x)/(1 + exp(x))
- *
- * gsl_sf_fermi_dirac_0(X) computes the complete Fermi-Dirac integral
- * with an index of 0:
- * F_0(x) = log(1 + exp(x))
- *
- * gsl_sf_fermi_dirac_1(X) computes the complete Fermi-Dirac integral
- * with an index of 1:
- * F_1(x) = \int_0^\infty t/(exp(t - x) + 1) dt
- *
- * gsl_sf_fermi_dirac_2(X) computes the complete Fermi-Dirac integral
- * with an index of 2:
- * F_2(x) = (1/2) \int_0^\infty t^2/(exp(t - x) + 1) dt
- *
- * gsl_sf_fermi_dirac_mhalf(X) computes the complete Fermi-Dirac integral
- * with an index of -1/2.
- *
- * gsl_sf_fermi_dirac_half(X) computes the complete Fermi-Dirac integral
- * with an index of +1/2.
- *
- * gsl_sf_fermi_dirac_3half(X) computes the complete Fermi-Dirac integral
- * with an index of +3/2.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf, gsl_sf_gamma.
+ gsl_sf_fermi_dirac_m1(x [, err])
+ gsl_sf_fermi_dirac_0(x [, err])
+ gsl_sf_fermi_dirac_1(x [, err])
+ gsl_sf_fermi_dirac_2(x [, err])
+ gsl_sf_fermi_dirac_mhalf(x [, err])
+ gsl_sf_fermi_dirac_half(x [, err])
+ gsl_sf_fermi_dirac_3half(x [, err])
+
+ gsl_sf_fermi_dirac_int(J,X) computes the complete Fermi-Dirac integral
+ with an index of J:
+ F_j(x) = 1/Gamma(j + 1) \int_0^\infty t^j/(exp(t - x) + 1) dt
+ where J is a scalar integer and Gamma() is the Gamma function:
+ Gamma(n) = (n - 1)!
+ for integer n.
+
+ gsl_sf_fermi_dirac_m1(X) computes the complete Fermi-Dirac integral with
+ an index of -1:
+ F_{-1}(x) = exp(x)/(1 + exp(x))
+
+ gsl_sf_fermi_dirac_0(X) computes the complete Fermi-Dirac integral with
+ an index of 0:
+ F_0(x) = log(1 + exp(x))
+
+ gsl_sf_fermi_dirac_1(X) computes the complete Fermi-Dirac integral with
+ an index of 1:
+ F_1(x) = \int_0^\infty t/(exp(t - x) + 1) dt
+
+ gsl_sf_fermi_dirac_2(X) computes the complete Fermi-Dirac integral with
+ an index of 2:
+ F_2(x) = (1/2) \int_0^\infty t^2/(exp(t - x) + 1) dt
+
+ gsl_sf_fermi_dirac_mhalf(X) computes the complete Fermi-Dirac integral
+ with an index of -1/2.
+
+ gsl_sf_fermi_dirac_half(X) computes the complete Fermi-Dirac integral
+ with an index of +1/2.
+
+ gsl_sf_fermi_dirac_3half(X) computes the complete Fermi-Dirac integral
+ with an index of +3/2.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf, gsl_sf_gamma.
*/
extern gsl_sf_gamma;
@@ -661,35 +658,35 @@ extern gsl_sf_gammastar;
extern gsl_sf_gammainv;
extern gsl_sf_taylorcoeff;
/* DOCUMENT gsl_sf_gamma(x [, err])
- * gsl_sf_lngamma(x [, err])
- * gsl_sf_gammastar(x [, err])
- * gsl_sf_gammainv(x [, err])
- * gsl_sf_taylorcoeff(n, x [, err])
- *
- * gsl_sf_gamma(X) computes the Gamma function:
- * Gammma(x) = \int_0^\infty t^(x - 1) exp(-t) dt for x >= 0
- * for a positive integer argument, Gamma(n) = (n - 1)!.
- *
- * gsl_sf_lngamma(X) computes the logarithm of the Gamma function.
- *
- * gsl_sf_gammastar(X) computes the regulated Gamma function:
- * GammaStar(x) = Gamma(x) / ( sqrt(2 pi) x^(x - 1/2) exp(x) )
- * = 1 + 1/12x + ... for large x
- *
- * gsl_sf_gammainv(X) computes the reciprocal of the Gamma function
- * 1/Gamma(x) using the real Lanczos method.
- *
- * gsl_sf_taylorcoeff(N,X) computes the Taylor coefficient X^N/N!
- * for X >= 0 and N >= 0 -- N must be a scalar integer.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_lngamma(x [, err])
+ gsl_sf_gammastar(x [, err])
+ gsl_sf_gammainv(x [, err])
+ gsl_sf_taylorcoeff(n, x [, err])
+
+ gsl_sf_gamma(X) computes the Gamma function:
+ Gammma(x) = \int_0^\infty t^(x - 1) exp(-t) dt for x >= 0
+ for a positive integer argument, Gamma(n) = (n - 1)!.
+
+ gsl_sf_lngamma(X) computes the logarithm of the Gamma function.
+
+ gsl_sf_gammastar(X) computes the regulated Gamma function:
+ GammaStar(x) = Gamma(x) / ( sqrt(2 pi) x^(x - 1/2) exp(x) )
+ = 1 + 1/12x + ... for large x
+
+ gsl_sf_gammainv(X) computes the reciprocal of the Gamma function
+ 1/Gamma(x) using the real Lanczos method.
+
+ gsl_sf_taylorcoeff(N,X) computes the Taylor coefficient X^N/N! for
+ X >= 0 and N >= 0 -- N must be a scalar integer.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
extern gsl_sf_psi;
@@ -697,42 +694,43 @@ extern gsl_sf_psi_1piy;
extern gsl_sf_psi_1;
extern gsl_sf_psi_n;
/* DOCUMENT gsl_sf_psi(x [, err])
- * gsl_sf_psi_1(x [, err])
- * gsl_sf_psi_n(n, x [, err])
- * gsl_sf_psi_1piy(x [, err])
- *
- * gsl_sf_psi(X) computes the digamma function \psi(x) for X != 0.
- *
- * gsl_sf_psi_1piy(Y) computes the real part of the digamma function on the
- * line 1+i y, \Re[\psi(1 + i y)].
- *
- * gsl_sf_psi_1(X) computes the trigamma function \psi'(x) for X.
- *
- * gsl_sf_psi_n(N, X) computes the polygamma function \psi^{(n)}(x)
- * for N >= 0, X > 0.
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_psi_1(x [, err])
+ gsl_sf_psi_n(n, x [, err])
+ gsl_sf_psi_1piy(x [, err])
+
+ gsl_sf_psi(X) computes the digamma function \psi(x) for X != 0.
+
+ gsl_sf_psi_1piy(Y) computes the real part of the digamma function on the
+ line 1+i y, \Re[\psi(1 + i y)].
+
+ gsl_sf_psi_1(X) computes the trigamma function \psi'(x) for X.
+
+ gsl_sf_psi_n(N, X) computes the polygamma function \psi^{(n)}(x)
+ for N >= 0, X > 0.
+
+ SEE ALSO: gsl_sf.
*/
local gsl_sf_lambert;
extern gsl_sf_lambert_W0;
extern gsl_sf_lambert_Wm1;
/* DOCUMENT gsl_sf_lambert_W0(x [, err])
- * gsl_sf_lambert_Wm1(x [, err])
- * Lambert's W functions, W(x), are defined to be solutions of the
- * equation W(x) exp(W(x)) = x. This function has multiple branches for
- * x < 0; however, it has only two real-valued branches. We define W0(x)
- * to be the principal branch, where W > -1 for x < 0, and Wm1(x) to
- * be the other real branch, where W < -1 for x < 0.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_lambert_Wm1(x [, err])
+
+ Lambert's W functions, W(x), are defined to be solutions of the equation
+ W(x) exp(W(x)) = x. This function has multiple branches for x < 0;
+ however, it has only two real-valued branches. We define W0(x) to be the
+ principal branch, where W > -1 for x < 0, and Wm1(x) to be the other real
+ branch, where W < -1 for x < 0.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
local gsl_sf_legendre;
@@ -744,27 +742,27 @@ extern gsl_sf_legendre_Q0;
extern gsl_sf_legendre_Q1;
extern gsl_sf_legendre_Ql;
/* DOCUMENT gsl_sf_legendre_P1(x [, err])
- * gsl_sf_legendre_P2(x [, err])
- * gsl_sf_legendre_P3(x [, err])
- * gsl_sf_legendre_Pl(l, x [, err])
- * gsl_sf_legendre_Q0(x [, err])
- * gsl_sf_legendre_Q1(x [, err])
- * gsl_sf_legendre_Ql(l, x [, err])
- *
- * The functions gsl_sf_legendre_P# evaluate the Legendre polynomials
- * P_l(x) for specific values of l = 1, 2, 3 or for a scalar integer l.
- *
- * The functions gsl_sf_legendre_Q# evaluate the Legendre function
- * Q_l(x) for specific values of l = 0, 1 or for a scalar integer l.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_legendre_P2(x [, err])
+ gsl_sf_legendre_P3(x [, err])
+ gsl_sf_legendre_Pl(l, x [, err])
+ gsl_sf_legendre_Q0(x [, err])
+ gsl_sf_legendre_Q1(x [, err])
+ gsl_sf_legendre_Ql(l, x [, err])
+
+ The functions gsl_sf_legendre_P# evaluate the Legendre polynomials P_l(x)
+ for specific values of l = 1, 2, 3 or for a scalar integer l.
+
+ The functions gsl_sf_legendre_Q# evaluate the Legendre function Q_l(x)
+ for specific values of l = 0, 1 or for a scalar integer l.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
local gsl_sf_synchrotron;
@@ -776,29 +774,29 @@ extern gsl_sf_transport_3;
extern gsl_sf_transport_4;
extern gsl_sf_transport_5;
/* DOCUMENT gsl_sf_synchrotron_1(x [, err])
- * gsl_sf_synchrotron_2(x [, err])
- * gsl_sf_transport_2(x [, err])
- * gsl_sf_transport_3(x [, err])
- * gsl_sf_transport_4(x [, err])
- * gsl_sf_transport_5(x [, err])
- *
- * gsl_sf_synchrotron_1(x) computes the first synchrotron function:
- * x \int_x^\infty K_{5/3}(t) dt for x >= 0.
- *
- * gsl_sf_synchrotron_2(x) computes the second synchrotron function:
- * x K_{2/3}(x) for x >= 0.
- *
- * The transport functions J(n,x) are defined by the integral representations:
- * J(n,x) = \int_0^x t^n e^t /(e^t - 1)^2 dt.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_synchrotron_2(x [, err])
+ gsl_sf_transport_2(x [, err])
+ gsl_sf_transport_3(x [, err])
+ gsl_sf_transport_4(x [, err])
+ gsl_sf_transport_5(x [, err])
+
+ gsl_sf_synchrotron_1(x) computes the first synchrotron function:
+ x \int_x^\infty K_{5/3}(t) dt for x >= 0.
+
+ gsl_sf_synchrotron_2(x) computes the second synchrotron function:
+ x K_{2/3}(x) for x >= 0.
+
+ The transport functions J(n,x) are defined by the integral representations:
+ J(n,x) = \int_0^x t^n e^t /(e^t - 1)^2 dt.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
extern gsl_sf_sin;
@@ -807,54 +805,54 @@ extern gsl_sf_sinc;
extern gsl_sf_lnsinh;
extern gsl_sf_lncosh;
/* DOCUMENT gsl_sf_sin(x [, err])
- * gsl_sf_cos(x [, err])
- * gsl_sf_sinc(x [, err])
- * gsl_sf_lnsinh(x [, err])
- * gsl_sf_lncosh(x [, err])
- *
- * gsl_sf_sin(X) computes the sine function of X.
- *
- * gsl_sf_cos(X) computes the cosine function of X.
- *
- * gsl_sf_sinc(X) computes sinc(x) = sin(pi x)/(pi x) for any value of X.
- *
- * gsl_sf_lnsinh(X) computes log(sinh(X)) for X > 0.
- *
- * gsl_sf_lncosh(X) computes log(cosh(X)) for any value of X.
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_cos(x [, err])
+ gsl_sf_sinc(x [, err])
+ gsl_sf_lnsinh(x [, err])
+ gsl_sf_lncosh(x [, err])
+
+ gsl_sf_sin(X) computes the sine function of X.
+
+ gsl_sf_cos(X) computes the cosine function of X.
+
+ gsl_sf_sinc(X) computes sinc(x) = sin(pi x)/(pi x) for any value of X.
+
+ gsl_sf_lnsinh(X) computes log(sinh(X)) for X > 0.
+
+ gsl_sf_lncosh(X) computes log(cosh(X)) for any value of X.
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
extern gsl_sf_zeta;
extern gsl_sf_zetam1;
extern gsl_sf_eta;
/* DOCUMENT gsl_sf_zeta(x [, err])
- * gsl_sf_zetam1(x [, err])
- * gsl_sf_eta(x [, err])
- *
- * gsl_sf_zeta(x) computes the Riemann zeta function:
- * zeta(x) = \sum_{k=1}^\infty k^{-x} for X != 1.
- *
- * gsl_sf_zetam1(x) computes zeta(X) - 1 for X != 1.
- *
- * gsl_sf_eta(x) computes the eta function:
- * eta(x) = (1 - 2^(1-x)) zeta(x).
- *
- * If optional argument ERR is true, the result, says Y, has an
- * additional dimension of length 2 prepended to the dimension list of X
- * which is used to provide an estimate of the error:
- * Y(1,..) = value of F(X)
- * Y(2,..) = error estimate for the value of F(X)
- *
- *
- * SEE ALSO: gsl_sf.
+ gsl_sf_zetam1(x [, err])
+ gsl_sf_eta(x [, err])
+
+ gsl_sf_zeta(x) computes the Riemann zeta function:
+ zeta(x) = \sum_{k=1}^\infty k^{-x} for X != 1.
+
+ gsl_sf_zetam1(x) computes zeta(X) - 1 for X != 1.
+
+ gsl_sf_eta(x) computes the eta function:
+ eta(x) = (1 - 2^(1-x)) zeta(x).
+
+ If optional argument ERR is true, the result, says Y, has an additional
+ dimension of length 2 prepended to the dimension list of X which is used
+ to provide an estimate of the error:
+ Y(1,..) = value of F(X)
+ Y(2,..) = error estimate for the value of F(X)
+
+
+ SEE ALSO: gsl_sf.
*/
extern gsl_poly_solve_quadratic;
@@ -864,9 +862,9 @@ extern gsl_poly_solve_cubic;
or x = gsl_poly_solve_cubic(a, b, c);
or x = gsl_poly_solve_cubic(v);
- These functions return the real roots of a quadratic or cubic polynomials
- with real coefficients A, B and C. When called with a single argument,
- it must be a vector of coefficients: V = [A,B,C].
+ These functions return the real roots of a quadratic or cubic
+ polynomials with real coefficients A, B and C. When called with a
+ single argument, it must be a vector of coefficients: V = [A,B,C].
If there are no roots, an empty result is returned otherwise a vector of
1, 2, or 3 roots is returned. The roots are sorted in ascending order.
@@ -883,14 +881,3 @@ extern gsl_poly_solve_cubic;
for a quadratic and a cubic polynomial respectively.
*/
-
-/*
- * Local Variables:
- * mode: Yorick
- * tab-width: 8
- * c-basic-offset: 2
- * indent-tabs-mode: nil
- * fill-column: 78
- * coding: utf-8
- * End:
- */
diff --git a/ygsl.c b/ygsl.c
index 004b073..d035c05 100644
--- a/ygsl.c
+++ b/ygsl.c
@@ -5,7 +5,7 @@
*
*-----------------------------------------------------------------------------
*
- * Copyright (C) 2012 Éric Thiébaut <eric.thiebaut at univ-lyon1.fr>
+ * Copyright (C) 2012-2016 Éric Thiébaut <eric.thiebaut at univ-lyon1.fr>
*
* This software is governed by the CeCILL-C license under French law and
* abiding by the rules of distribution of free software. You can use, modify
@@ -573,15 +573,3 @@ void Y_gsl_poly_solve_cubic(int argc)
n = gsl_poly_solve_cubic(a, b, c, &x[0], &x[1], &x[2]);
push_vector_d(n, x);
}
-
-/*
- * Local Variables:
- * mode: C
- * c-basic-offset: 2
- * tab-width: 8
- * indent-tabs-mode: nil
- * fill-column: 78
- * coding: utf-8
- * ispell-local-dictionary: "american"
- * End:
- */
--
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