fermi_dirac.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* specfunc/fermi_dirac.c
 * 
 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
 * 
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */

/* Author:  G. Jungman */

#include <config.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_exp.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_sf_hyperg.h>
#include <gsl/gsl_sf_pow_int.h>
#include <gsl/gsl_sf_zeta.h>
#include <gsl/gsl_sf_fermi_dirac.h>

#include "error.h"

#include "chebyshev.h"
#include "cheb_eval.c"

#define locEPS  (1000.0*GSL_DBL_EPSILON)


/* Chebyshev fit for F_{1}(t);  -1 < t < 1, -1 < x < 1
 */
static double fd_1_a_data[22] = {
  1.8949340668482264365,
  0.7237719066890052793,
  0.1250000000000000000,
  0.0101065196435973942,
  0.0,
 -0.0000600615242174119,
  0.0,
  6.816528764623e-7,
  0.0,
 -9.5895779195e-9,
  0.0,
  1.515104135e-10,
  0.0,
 -2.5785616e-12,
  0.0,
  4.62270e-14,
  0.0,
 -8.612e-16,
  0.0,
  1.65e-17,
  0.0,
 -3.e-19
};
static cheb_series fd_1_a_cs = {
  fd_1_a_data,
  21,
  -1, 1,
  12
};


/* Chebyshev fit for F_{1}(3/2(t+1) + 1);  -1 < t < 1, 1 < x < 4
 */
static double fd_1_b_data[22] = {
  10.409136795234611872,
  3.899445098225161947,
  0.513510935510521222,
  0.010618736770218426,
 -0.001584468020659694,
  0.000146139297161640,
 -1.408095734499e-6,
 -2.177993899484e-6,
  3.91423660640e-7,
 -2.3860262660e-8,
 -4.138309573e-9,
  1.283965236e-9,
 -1.39695990e-10,
 -4.907743e-12,
  4.399878e-12,
 -7.17291e-13,
  2.4320e-14,
  1.4230e-14,
 -3.446e-15,
  2.93e-16,
  3.7e-17,
 -1.6e-17
};
static cheb_series fd_1_b_cs = {
  fd_1_b_data,
  21,
  -1, 1,
  11
};


/* Chebyshev fit for F_{1}(3(t+1) + 4);  -1 < t < 1, 4 < x < 10
 */
static double fd_1_c_data[23] = {
  56.78099449124299762,
  21.00718468237668011,
  2.24592457063193457,
  0.00173793640425994,
 -0.00058716468739423,
  0.00016306958492437,
 -0.00003817425583020,
  7.64527252009e-6,
 -1.31348500162e-6,
  1.9000646056e-7,
 -2.141328223e-8,
  1.23906372e-9,
  2.1848049e-10,
 -1.0134282e-10,
  2.484728e-11,
 -4.73067e-12,
  7.3555e-13,
 -8.740e-14,
  4.85e-15,
  1.23e-15,
 -5.6e-16,
  1.4e-16,
 -3.e-17
};
static cheb_series fd_1_c_cs = {
  fd_1_c_data,
  22,
  -1, 1,
  13
};


/* Chebyshev fit for F_{1}(x) / x^2
 * 10 < x < 30 
 * -1 < t < 1
 * t = 1/10 (x-10) - 1 = x/10 - 2
 * x = 10(t+2)
 */
static double fd_1_d_data[30] = {
  1.0126626021151374442,
 -0.0063312525536433793,
  0.0024837319237084326,
 -0.0008764333697726109,
  0.0002913344438921266,
 -0.0000931877907705692,
  0.0000290151342040275,
 -8.8548707259955e-6,
  2.6603474114517e-6,
 -7.891415690452e-7,
  2.315730237195e-7,
 -6.73179452963e-8,
  1.94048035606e-8,
 -5.5507129189e-9,
  1.5766090896e-9,
 -4.449310875e-10,
  1.248292745e-10,
 -3.48392894e-11,
  9.6791550e-12,
 -2.6786240e-12,
  7.388852e-13,
 -2.032828e-13,
  5.58115e-14,
 -1.52987e-14,
  4.1886e-15,
 -1.1458e-15,
  3.132e-16,
 -8.56e-17,
  2.33e-17,
 -5.9e-18
};
static cheb_series fd_1_d_cs = {
  fd_1_d_data,
  29,
  -1, 1,
  14
};


/* Chebyshev fit for F_{1}(x) / x^2
 * 30 < x < Inf
 * -1 < t < 1
 * t = 60/x - 1
 * x = 60/(t+1)
 */
static double fd_1_e_data[10] = {
  1.0013707783890401683,
  0.0009138522593601060,
  0.0002284630648400133,
 -1.57e-17,
 -1.27e-17,
 -9.7e-18,
 -6.9e-18,
 -4.6e-18,
 -2.9e-18,
 -1.7e-18
};
static cheb_series fd_1_e_cs = {
  fd_1_e_data,
  9,
  -1, 1,
  4
};


/* Chebyshev fit for F_{2}(t);  -1 < t < 1, -1 < x < 1
 */
static double fd_2_a_data[21] = {
  2.1573661917148458336,
  0.8849670334241132182,
  0.1784163467613519713,
  0.0208333333333333333,
  0.0012708226459768508,
  0.0,
 -5.0619314244895e-6,
  0.0,
  4.32026533989e-8,
  0.0,
 -4.870544166e-10,
  0.0,
  6.4203740e-12,
  0.0,
 -9.37424e-14,
  0.0,
  1.4715e-15,
  0.0,
 -2.44e-17,
  0.0,
  4.e-19
};
static cheb_series fd_2_a_cs = {
  fd_2_a_data,
  20,
  -1, 1,
  12
};


/* Chebyshev fit for F_{2}(3/2(t+1) + 1);  -1 < t < 1, 1 < x < 4
 */
static double fd_2_b_data[22] = {
  16.508258811798623599,
  7.421719394793067988,
  1.458309885545603821,
  0.128773850882795229,
  0.001963612026198147,
 -0.000237458988738779,
  0.000018539661382641,
 -1.92805649479e-7,
 -2.01950028452e-7,
  3.2963497518e-8,
 -1.885817092e-9,
 -2.72632744e-10,
  8.0554561e-11,
 -8.313223e-12,
 -2.24489e-13,
  2.18778e-13,
 -3.4290e-14,
  1.225e-15,
  5.81e-16,
 -1.37e-16,
  1.2e-17,
  1.e-18
};
static cheb_series fd_2_b_cs = {
  fd_2_b_data,
  21,
  -1, 1,
  12
};


/* Chebyshev fit for F_{1}(3(t+1) + 4);  -1 < t < 1, 4 < x < 10
 */
static double fd_2_c_data[20] = {
  168.87129776686440711,
  81.80260488091659458,
  15.75408505947931513,
  1.12325586765966440,
  0.00059057505725084,
 -0.00016469712946921,
  0.00003885607810107,
 -7.89873660613e-6,
  1.39786238616e-6,
 -2.1534528656e-7,
  2.831510953e-8,
 -2.94978583e-9,
  1.6755082e-10,
  2.234229e-11,
 -1.035130e-11,
  2.41117e-12,
 -4.3531e-13,
  6.447e-14,
 -7.39e-15,
  4.3e-16
};
static cheb_series fd_2_c_cs = {
  fd_2_c_data,
  19,
  -1, 1,
  12
};


/* Chebyshev fit for F_{1}(x) / x^3
 * 10 < x < 30 
 * -1 < t < 1
 * t = 1/10 (x-10) - 1 = x/10 - 2
 * x = 10(t+2)
 */
static double fd_2_d_data[30] = {
  0.3459960518965277589,
 -0.00633136397691958024,
  0.00248382959047594408,
 -0.00087651191884005114,
  0.00029139255351719932,
 -0.00009322746111846199,
  0.00002904021914564786,
 -8.86962264810663e-6,
  2.66844972574613e-6,
 -7.9331564996004e-7,
  2.3359868615516e-7,
 -6.824790880436e-8,
  1.981036528154e-8,
 -5.71940426300e-9,
  1.64379426579e-9,
 -4.7064937566e-10,
  1.3432614122e-10,
 -3.823400534e-11,
  1.085771994e-11,
 -3.07727465e-12,
  8.7064848e-13,
 -2.4595431e-13,
  6.938531e-14,
 -1.954939e-14,
  5.50162e-15,
 -1.54657e-15,
  4.3429e-16,
 -1.2178e-16,
  3.394e-17,
 -8.81e-18
};
static cheb_series fd_2_d_cs = {
  fd_2_d_data,
  29,
  -1, 1,
  14
};


/* Chebyshev fit for F_{2}(x) / x^3
 * 30 < x < Inf
 * -1 < t < 1
 * t = 60/x - 1
 * x = 60/(t+1)
 */
static double fd_2_e_data[4] = {
  0.3347041117223735227,
  0.00091385225936012645,
  0.00022846306484003205,
  5.2e-19
};
static cheb_series fd_2_e_cs = {
  fd_2_e_data,
  3,
  -1, 1,
  3
};


/* Chebyshev fit for F_{-1/2}(t);  -1 < t < 1, -1 < x < 1
 */
static double fd_mhalf_a_data[20] = {
  1.2663290042859741974,
  0.3697876251911153071,
  0.0278131011214405055,
 -0.0033332848565672007,
 -0.0004438108265412038,
  0.0000616495177243839,
  8.7589611449897e-6,
 -1.2622936986172e-6,
 -1.837464037221e-7,
  2.69495091400e-8,
  3.9760866257e-9,
 -5.894468795e-10,
 -8.77321638e-11,
  1.31016571e-11,
  1.9621619e-12,
 -2.945887e-13,
 -4.43234e-14,
  6.6816e-15,
  1.0084e-15,
 -1.561e-16
};
static cheb_series fd_mhalf_a_cs = {
  fd_mhalf_a_data,
  19,
  -1, 1,
  12
};


/* Chebyshev fit for F_{-1/2}(3/2(t+1) + 1);  -1 < t < 1, 1 < x < 4
 */
static double fd_mhalf_b_data[20] = {
  3.270796131942071484,
  0.5809004935853417887,
 -0.0299313438794694987,
 -0.0013287935412612198,
  0.0009910221228704198,
 -0.0001690954939688554,
  6.5955849946915e-6,
  3.5953966033618e-6,
 -9.430672023181e-7,
  8.75773958291e-8,
  1.06247652607e-8,
 -4.9587006215e-9,
  7.160432795e-10,
  4.5072219e-12,
 -2.3695425e-11,
  4.9122208e-12,
 -2.905277e-13,
 -9.59291e-14,
  3.00028e-14,
 -3.4970e-15
};
static cheb_series fd_mhalf_b_cs = {
  fd_mhalf_b_data,
  19,
  -1, 1,
  12
};


/* Chebyshev fit for F_{-1/2}(3(t+1) + 4);  -1 < t < 1, 4 < x < 10
 */
static double fd_mhalf_c_data[25] = {
  5.828283273430595507,
  0.677521118293264655,
 -0.043946248736481554,
  0.005825595781828244,
 -0.000864858907380668,
  0.000110017890076539,
 -6.973305225404e-6,
 -1.716267414672e-6,
  8.59811582041e-7,
 -2.33066786976e-7,
  4.8503191159e-8,
 -8.130620247e-9,
  1.021068250e-9,
 -5.3188423e-11,
 -1.9430559e-11,
  8.750506e-12,
 -2.324897e-12,
  4.83102e-13,
 -8.1207e-14,
  1.0132e-14,
 -4.64e-16,
 -2.24e-16,
  9.7e-17,
 -2.6e-17,
  5.e-18
};
static cheb_series fd_mhalf_c_cs = {
  fd_mhalf_c_data,
  24,
  -1, 1,
  13
};


/* Chebyshev fit for F_{-1/2}(x) / x^(1/2)
 * 10 < x < 30 
 * -1 < t < 1
 * t = 1/10 (x-10) - 1 = x/10 - 2
 */
static double fd_mhalf_d_data[30] = {
  2.2530744202862438709,
  0.0018745152720114692,
 -0.0007550198497498903,
  0.0002759818676644382,
 -0.0000959406283465913,
  0.0000324056855537065,
 -0.0000107462396145761,
  3.5126865219224e-6,
 -1.1313072730092e-6,
  3.577454162766e-7,
 -1.104926666238e-7,
  3.31304165692e-8,
 -9.5837381008e-9,
  2.6575790141e-9,
 -7.015201447e-10,
  1.747111336e-10,
 -4.04909605e-11,
  8.5104999e-12,
 -1.5261885e-12,
  1.876851e-13,
  1.00574e-14,
 -1.82002e-14,
  8.6634e-15,
 -3.2058e-15,
  1.0572e-15,
 -3.259e-16,
  9.60e-17,
 -2.74e-17,
  7.6e-18,
 -1.9e-18
};
static cheb_series fd_mhalf_d_cs = {
  fd_mhalf_d_data,
  29,
  -1, 1,
  15
};


/* Chebyshev fit for F_{1/2}(t);  -1 < t < 1, -1 < x < 1
 */
static double fd_half_a_data[23] = {
  1.7177138871306189157,
  0.6192579515822668460,
  0.0932802275119206269,
  0.0047094853246636182,
 -0.0004243667967864481,
 -0.0000452569787686193,
  5.2426509519168e-6,
  6.387648249080e-7,
 -8.05777004848e-8,
 -1.04290272415e-8,
  1.3769478010e-9,
  1.847190359e-10,
 -2.51061890e-11,
 -3.4497818e-12,
  4.784373e-13,
  6.68828e-14,
 -9.4147e-15,