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

C. S. Jog ()
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C. S. Jog: Indian Institute of Science

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 451-462

Abstract: Abstract We present a Fourier-series based method for deriving alternative expressions for $$\zeta (2m)$$ 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.

Keywords: Riemann zeta function at even integers; Zeros of Bessel functions; 11M06 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00377-3

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