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'''Generalized polygamma function''' is a function, introduced by Olivier Espinosa and Victor H. Moll<ref>[http://www.math.tulane.edu/~vhm/papers_html/genoff.pdf Olivier Espinosa Victor H. Moll. A Generalized polygamma function. Integral Transforms and Special Functions Vol. 15, No. 2, April 2004, pp. 101–115
It is defined as follows:
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