| @cindex Debye functions |
| |
| The Debye functions @math{D_n(x)} are defined by the following integral, |
| @tex |
| \beforedisplay |
| $$ |
| D_n(x) = {n \over x^n} \int_0^x dt {t^n \over e^t - 1} |
| $$ |
| \afterdisplay |
| @end tex |
| @ifinfo |
| |
| @example |
| D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1)) |
| @end example |
| |
| @end ifinfo |
| @noindent |
| For further information see Abramowitz & |
| Stegun, Section 27.1. The Debye functions are declared in the header |
| file @file{gsl_sf_debye.h}. |
| |
| @deftypefun double gsl_sf_debye_1 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_1_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the first-order Debye function |
| @math{D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_debye_2 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_2_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the second-order Debye function |
| @math{D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_debye_3 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_3_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the third-order Debye function |
| @math{D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_debye_4 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_4_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the fourth-order Debye function |
| @math{D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_debye_5 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_5_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the fifth-order Debye function |
| @math{D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW |
| @end deftypefun |
| |
| @deftypefun double gsl_sf_debye_6 (double @var{x}) |
| @deftypefunx int gsl_sf_debye_6_e (double @var{x}, gsl_sf_result * @var{result}) |
| These routines compute the sixth-order Debye function |
| @math{D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1))}. |
| @comment Exceptional Return Values: GSL_EDOM, GSL_EUNDRFLW |
| @end deftypefun |