Balanced polygamma function: Difference between revisions

Revision as of 18:42, 18 November 2009

Revision as of 18:45, 18 November 2009

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It is defined as follows:

<math>\psi(z,q)=\frac{\zeta'(z+1,q)+(\psi(-z)+\gamma ) \zeta (z+1,q)}{\Gamma (-z)}</math>

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Several special functions can be expressed in terms of generalized polygamma function.

* <math>\psi(x)=\psi(0,x)\,</math>

* <math>\psi^{(n)}(x)=\psi(n,x)\,\,\,(n\in\mathbb{N})</math>