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m Anuclanus moved page Generalized polygamma function to Balanced polygamma function |
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In mathematics, the '''generalized polygamma function''' or '''balanced negapolygamma function''' is a function introduced by Olivier Espinosa and [[Victor Moll|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]</ref> It generalizes the [[polygamma function]] to negative and fractional order, but remains equal to it for integer positive orders. The function is balanced, that is satisfies the conditions $f(0)=f(1)$ and $\int_0^1 f(x) dx = 0$.
It is defined as follows:
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