caa a22 4500 445868880 CHVBK 20180317145506.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00605-010-0208-x doi (NATIONALLICENCE)springer-10.1007/s00605-010-0208-x Dixit Atul Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, IL, USA aut Transformation formulas associated with integrals involving the Riemann Ξ-function [Elektronische Daten] [Atul Dixit] Using residue calculus and the theory of Mellin transforms, we evaluate integrals of a certain type involving the Riemann Ξ-function, which give transformation formulas of the form F(z, α) = F(z, β), where αβ = 1. This gives a unified approach for generating certain modular transformation formulas, including a famous formula of Ramanujan and Guinand. Springer-Verlag, 2010 Riemann Ξ-function nationallicence Hurwitz zeta function nationallicence Modified Bessel function nationallicence Residue theorem nationallicence Mellin transform nationallicence Ramanujan nationallicence Monatshefte für Mathematik Springer Vienna 164/2(2011-10-01), 133-156 0026-9255 164:2<133 2011 164 605 https://doi.org/10.1007/s00605-010-0208-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0208-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dixit Atul Department of Mathematics, University of Illinois, 1409 West Green Street, 61801, Urbana, IL, USA aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 164/2(2011-10-01), 133-156 0026-9255 164:2<133 2011 164 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer