Alternative expressions for the Riemann zeta and related functions at positive even integers and infinite sums involving zeros of Bessel and spherical Bessel functions of the first kind

Jog, CS (2023) Alternative expressions for the Riemann zeta and related functions at positive even integers and infinite sums involving zeros of Bessel and spherical Bessel functions of the first kind. In: Indian Journal of Pure and Applied Mathematics .

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Abstract

We present a Fourier-series based method for deriving alternative expressions for ζ(2 m) and related functions such as the Dirichlet eta function, and the Bernoulli and Euler numbers. Using this method, we also present generalizations of known results for infinite sums involving the zeros of Bessel functions of the first kind. © 2023, The Indian National Science Academy.

Item Type:	Journal Article
Publication:	Indian Journal of Pure and Applied Mathematics
Publisher:	Indian National Science Academy
Additional Information:	The copyright for this article belongs to Indian National Science Academy.
Keywords:	Riemann zeta function at even integers; Zeros of Bessel functions
Department/Centre:	Division of Mechanical Sciences > Mechanical Engineering
Date Deposited:	16 Feb 2023 05:26
Last Modified:	16 Feb 2023 05:26
URI:	https://eprints.iisc.ac.in/id/eprint/80311

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