Debye functions.

Ed Smith-Rowland
Fri Mar 24 09:20:00 GMT 2017


I've been looking at the Debye integrals

D_n(x) = \frac{n}{x^n}\int_{0}^{x} \frac{t^n}{e^t - 1}dt

The integrand is everywhere positive.

The definite integral must be zero for x=0.

The values returned by gsl debye functions start at one for x=0 and 
monotonically decrease.

The definite integral of a positive functions must start at zero and 
monotonically increase.

Is it possible that we have a complementary Debye integral? Perhaps scaled?

In any case, the functions can't match the formulas in the manual.

Thank you.

Ed Smith-Rowland

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