PolyGamma Functions of Negative Order

The article is published in Journal of Computational and Applied Mathematics, 100(1998),191--199.


  • Abstract

  • Liouville's fractional integration is used to define polygamma functions $\psi^{(n)}(z)$ for negative integer $n$. It's shown that such $\psi^{(n)}(z)$ can be represented in a closed form by means of the first derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed.

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  • Please send corrections to Victor S. Adamchik
    Computer Science Department, 
    Carnegie Mellon University, Pittsburgh, PA.