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- W1979235104 abstract "We obtain a variety of series and integral representations of the digamma function $psi(a)$. These in turn provide representations of the evaluations $psi(p/q)$ at rational argument and for the polygamma function $psi^{(j)}$. The approach is through a limit definition of the zeroth Stieltjes constant $gamma_0(a)=-psi(a)$. Several other results are obtained, including product representations for $exp[gamma_0(a)]$ and for the Gamma function $Gamma(a)$. In addition, we present series representations in terms of trigonometric integrals Ci and Si for $psi(a)$ and the Euler constant $gamma=-psi(1)$." @default.
- W1979235104 created "2016-06-24" @default.
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- W1979235104 date "2012-11-01" @default.
- W1979235104 modified "2023-09-24" @default.
- W1979235104 title "Integral and series representations of the digamma and polygamma functions" @default.
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- W1979235104 doi "https://doi.org/10.1524/anly.2012.1130" @default.
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