Koshliakov kernel and identities involving the Riemann zeta function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:435

Article

Dixit, Atul¹  Robles, Nicolas²  Roy, Arindam³  Zaharescu, Alexanchu^3,4 

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Univ Zurich, Inst Math, CH-8057 Zurich, Switzerland

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[4] Romanian Acad, Inst Math, RO-70700 Bucharest, Romania

关键词: Riemann zeta function;    Hurwitz zeta function;    Bessel functions;    Koshliakov;   

DOI  :  10.1016/j.jmaa.2015.11.007

来源: Elsevier

【 摘 要 】

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. Published by Elsevier Inc.

【 授权许可】

Free