Generalizations of a formula due to Kummer with applications

DOI10.2298/FIL2002671KzbMath1499.33028OpenAlexW3112691471WikidataQ115058622 ScholiaQ115058622MaRDI QIDQ5865645

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Publication date: 9 June 2022

Published in: Filomat (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2298/fil2002671k

zbMATH Keywords

generalized hypergeometric functionbeta integralRamanujan's identityKummer's formulaextension of Gauss second summation theorem

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Cites Work

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• Extensions of certain classical summation theorems for the series \(_2F_1\), \(_3F_2\) and with applications in Ramanujan's summations
• Generalized Watson's summation formula for \(_3F_2(1)\)
• Automatic generation of hypergeometric identities by the beta integral method.
• A generalization of Kummer's identity.
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• CERTAIN HYPERGEOMETRIC IDENTITIES DEDUCIBLE BY USING THE BETA INTEGRAL METHOD
• Generalization of Kummer’s second theorem with applications
• Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications
• A generalization of a formula due to Kummer^†
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• A study of generalized summation theorems for the series 2F1 with an applications to Laplace transforms of convolution type integrals involving Kummer's functions 1F1

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