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arXiv · 2205.08183

Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values

Parth Chavan
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Abstract

Inspired by a famous formula of Ramanujan for odd zeta values, we prove an analogous formula involving the Hurwitz zeta function. We introduce a new integral kernel related to the Hurwitz zeta function, generalizing the integral kernel associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula.

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Parth Chavan. 2022-05-17. Hurwitz Zeta Functions and Ramanujan's Identity for Odd Zeta Values. https://arxiv.org/abs/2205.08183

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