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In mathematics, the '''generalized polygamma function''' or '''balanced negapolygamma function''' is a function introduced by Olivier Espinosa Aldunate and [[Victor Hugo Moll]].<ref>{{cite journal|url=http://www.math.tulane.edu/~vhm/papers_html/genoff.pdf|first1=Olivier|last1=Espinosa|first2=Victor Hugo|last2=Moll |author-link2=Victor Hugo Moll |title=A Generalized polygamma function|journal=Integral Transforms and Special Functions|volume=15|issue=2|date=Apr 2004|
It generalizes the [[polygamma function]] to negative and fractional order, but remains equal to it for integer positive orders.
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