Series transformations and integrals involving the Riemann \(\Xi \)-function

DOI10.1016/j.jmaa.2010.03.047zbMath1206.11104OpenAlexW2074946841MaRDI QIDQ972489

Atul Dixit

Publication date: 19 May 2010

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.03.047

zbMATH Keywords

Mellin transformRiemann zeta-functionRamanujanmodified Bessel functionresidue theorempsi functionRiemann \(\Xi\)-functionHardy.

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (7)

ANALOGUES OF A TRANSFORMATION FORMULA OF RAMANUJAN ⋮ A Transformation Formula Involving the Gamma and Riemann Zeta Functions in Ramanujan’s Lost Notebook ⋮ 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 ⋮ A new integral equation and integrals associated with number theory ⋮ Koshliakov zeta functions I: modular relations

Cites Work

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• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• 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 Solutions of the Equation F (t ) = F (t ⁻¹ )
• Some Formulae for the Riemann Zeta-Function
• A note on the logarithmic derivative of the gamma function

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