GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) Get a printed copy>>>

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7.10 Debye Functions

The Debye functions D_n(x) are defined by the following integral,

D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1))

For further information see Abramowitz & Stegun, Section 27.1. The Debye functions are declared in the header file ‘gsl_sf_debye.h’.

Function: double gsl_sf_debye_1 (double x)

Function: int gsl_sf_debye_1_e (double x, gsl_sf_result * result)

These routines compute the first-order Debye function, which is defined as D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)).

Function: double gsl_sf_debye_2 (double x)

Function: int gsl_sf_debye_2_e (double x, gsl_sf_result * result)

These routines compute the second-order Debye function, which is defined as D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)).

Function: double gsl_sf_debye_3 (double x)

Function: int gsl_sf_debye_3_e (double x, gsl_sf_result * result)

These routines compute the third-order Debye function, which is defined as D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)).

Function: double gsl_sf_debye_4 (double x)

Function: int gsl_sf_debye_4_e (double x, gsl_sf_result * result)

These routines compute the fourth-order Debye function, which is defined as D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)).

Function: double gsl_sf_debye_5 (double x)

Function: int gsl_sf_debye_5_e (double x, gsl_sf_result * result)

These routines compute the fifth-order Debye function, which is defined as D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1)).

Function: double gsl_sf_debye_6 (double x)

Function: int gsl_sf_debye_6_e (double x, gsl_sf_result * result)

These routines compute the sixth-order Debye function, which is defined as D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1)).