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arXiv · 1702.05439

Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action

Omran Kouba
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Abstract

In this note, we recall Kummer's Fourier series expansion of the 1-periodic function that coincides with the logarithm of the Gamma function on the unit interval $(0,1)$, and we use it to find closed forms for some numerical series related to the generalized Stieltjes constants, and some integrals involving the function $x\mapsto \ln \ln(1/x)$.

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Omran Kouba. 2017-02-17. Generalized Stieltjes constants and integrals involving the log-log function: Kummer's Theorem in action. https://doi.org/10.7153/jca-09-09

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