Transformation formulas associated with integrals involving the Riemann \(\Xi\)-function

DOI10.1007/s00605-010-0208-xzbMath1246.11141OpenAlexW2110690143MaRDI QIDQ646619

Atul Dixit

Publication date: 17 November 2011

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-010-0208-x

zbMATH Keywords

Mellin transformHurwitz zeta functionRamanujanModified Bessel functionResidue theoremRiemann \(\Xi \)-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Hurwitz and Lerch zeta functions (11M35)

Related Items

New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan ⋮ Koshliakov kernel and identities involving the Riemann zeta function ⋮ Character analogues of Cohen-type identities and related Voronoï summation formulas ⋮ Transformation formulas associated with integrals involving the Riemann \(\Xi\)-function ⋮ Self-reciprocal functions, powers of the Riemann zeta function and modular-type transformations ⋮ Superimposing theta structure on a generalized modular relation ⋮ Extensions of Watson’s theorem and the Ramanujan–Guinand formula

Uses Software

• GL(n)pack

Cites Work

• Transformation formulas associated with integrals involving the Riemann \(\Xi\)-function
• Series transformations and integrals involving the Riemann \(\Xi \)-function
• ANALOGUES OF A TRANSFORMATION FORMULA OF RAMANUJAN
• A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook
• Koshliakovs Formula and Guinands Formula in Ramanujans Lost Notebook
• SOME SELF-RECIPROCAL FUNCTIONS
• SOME RAPIDLY CONVERGENT SERIES FOR THE RIEMANN ξ-FUNCTION
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