Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit; Nicolas Robles; Arindam Roy; Alexandru Zaharescu

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arXiv · 1505.01552

Koshliakov kernel and identities involving the Riemann zeta function

Atul Dixit·Nicolas Robles·Arindam Roy·Alexandru Zaharescu

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Abstract

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions $J_{z}(x), Y_{z}(x)$ and $K_{z}(x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.

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Atul Dixit, Nicolas Robles, Arindam Roy, Alexandru Zaharescu. 2015-05-07. Koshliakov kernel and identities involving the Riemann zeta function. https://arxiv.org/abs/1505.01552

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