Some Remarks on Glaisher-Ramanujan Type Integrals
Alexander E. Patkowski
TL;DR
This paper generalizes Glaisher-Ramanujan integrals, derives new Ramanujan-type series identities, and presents a novel formula for the Dirichlet beta function at s=3, expanding the analytical understanding of these special functions.
Contribution
The paper introduces a broader class of Glaisher-Ramanujan integrals and derives new series identities and a formula for the Dirichlet beta function at s=3.
Findings
Generalized Glaisher-Ramanujan integrals
New Ramanujan-type series identities
A new formula for the Dirichlet beta function at s=3
Abstract
Some integrals of the Glaisher-Ramanujan type are established in a more general form than in previous studies. As an application we prove some Ramanujan-type series identities, as well as a new formula for the Dirichlet beta function at the value
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