Hurwitz zeta functions and Ramanujan's identity for odd zeta values

被引：1

作者：

Chavan, Parth ^{[1
]}

机构：

[1] Euler Circle, Palo Alto, CA 94306 USA

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 527卷 / 02期

关键词：

Hurwitz zeta function; Ramanujan's formula for odd zeta; values; Dirichlet series;

D O I：

10.1016/j.jmaa.2023.127524

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 that associated to Ramanujan's identity. We also derive several infinite families of identities analogous to Ramanujan's formula. & COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：20

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