## File: Debye-Functions.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130  GNU Scientific Library – Reference Manual: Debye Functions

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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 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 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 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 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 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 D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1)).