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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.
These routines compute the first-order Debye function D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)).
These routines compute the second-order Debye function D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)).
These routines compute the third-order Debye function D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)).
These routines compute the fourth-order Debye function D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)).
These routines compute the fifth-order Debye function D_5(x) = (5/x^5) \int_0^x dt (t^5/(e^t - 1)).
These routines compute the sixth-order Debye function D_6(x) = (6/x^6) \int_0^x dt (t^6/(e^t - 1)).