A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook

DOI10.1007/978-1-4419-6263-8_12zbMath1322.11086arXiv0904.1053OpenAlexW1584385238MaRDI QIDQ3193076

Atul Dixit, Bruce C. Berndt

Publication date: 14 October 2015

Published in: The Legacy of Alladi Ramakrishnan in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.1053

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15)

Related Items (12)

Ramanujan's integral identities of the Riemann \(\Xi\)-function and the Lerch transcendent ⋮ ANALOGUES OF A TRANSFORMATION FORMULA OF RAMANUJAN ⋮ Koshliakov kernel and identities involving the Riemann zeta function ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ Multiple gamma functions, multiple sine functions, and Appell's \(O\)-functions ⋮ Transformation formulas associated with integrals involving the Riemann \(\Xi\)-function ⋮ Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations ⋮ Stirling modular forms and special values of multiple cotangent functions ⋮ Series transformations and integrals involving the Riemann \(\Xi \)-function ⋮ Superimposing theta structure on a generalized modular relation ⋮ Koshliakov zeta functions I: modular relations ⋮ Extended higher Herglotz function. II

Cites Work

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• Series transformations and integrals involving the Riemann \(\Xi \)-function
• On Poisson's summation formula
• ANALOGUES OF A TRANSFORMATION FORMULA OF RAMANUJAN
• Some Finite Identities Connected with Poisson's Summation Formula
• Ramanujan's Quarterly Reports
• Some Formulae for the Riemann Zeta-Function
• A note on the logarithmic derivative of the gamma function

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