Koshliakov kernel and identities involving the Riemann zeta function

2015/05/07 by Atul Dixit, Dixit, Atul, Nicolas Robles +5
Mathematics · #11M35 #33C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #Primary 11M06 #Secondary 33E20 #math.CA #math.NT #msc:11M06 #msc:11M35 #msc:33C10 #msc:33E20

paper · pdf · doi:10.48550/arxiv.1505.01552

21 pages, 5 figures; submitted for publication

arxiv created 2015/05/07 · arxiv updated 2015/05/08

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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