Some unified and generalized Kummer's first summation theorems with applications in Laplace transform technique

zbMath1348.33002MaRDI QIDQ326938

M. S. Baboo, Mohammad Idris Qureshi

Publication date: 12 October 2016

Published in: Asia Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://apjm.apacific.org/PDFs/3-1-10-23.pdf

zbMATH Keywords

Laplace transformsbeta and gamma functionsGauss and Kummer hypergeometric functionsLegendre duplication formulaprinciple of analytic continuation

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Integral transforms of special functions (44A20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (3)

Summation theorems for \({_p}F_{q+1}[(\alpha_p);g\pm m, (\beta_q); z\) via Mellin-Barnes type contour integral and its applications] ⋮ Summation theorems for \({_{p+1}}F_{q}[a\pm m, (\alpha_p); (\beta_q); z\) via Mellin-Barnes type contour integral and its applications] ⋮ Unnamed Item

Cites Work

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• Contiguous extensions of Dixon's theorem on the sum of a \(_3F_2\)
• Further results on Srivastava's triple hypergeometric series \(H_A\) and \(H_C\)
• New Laplace transforms of Kummer's confluent hypergeometric functions
• Kummer's theorem and its contiguous identities
• Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications
• A generalization of a formula due to Kummer^†

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