Polygamma Function - Integral Representation

Integral Representation

The polygamma function may be represented as

\psi^{(m)}(z)= (-1)^{m+1}\int_0^\infty \frac{t^m e^{-zt}} {1-e^{-t}} dt

which holds for Re z >0 and m > 0. For m = 0 see the digamma function definition.

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