Extensions of certain classical summation theorems for the series \(_2F_1\), \(_3F_2\) and with applications in Ramanujan's summations

DOI10.1155/2010/309503zbMath1210.33012OpenAlexW2145513873WikidataQ58651731 ScholiaQ58651731MaRDI QIDQ623684

Yong Sup Kim, Medhat A. Rakha, Arjun K. Rathie

Publication date: 8 February 2011

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2010/309503

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (22)

Unnamed Item ⋮ An alternative proof of the extended Saalschütz summation theorem for the _{r + 3} F _{r + 2} (1) series with applications ⋮ On an extension of Kummer's second theorem ⋮ A note on a further extension of Gauss’s second summation theorem with an application to the extension of two well-known combinatorial identities ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Generalization of a summation formula due to fox ⋮ A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications ⋮ An interesting integral involving product of two generalized hypergeometric function ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Applications of extended Watson's summation theorem ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A study of extensions of classical summation theorems for the series \(_3F_2\) and \(_4F_3\) with applications ⋮ Unnamed Item ⋮ On a new class of Laplace-type integrals involving generalized hypergeometric functions ⋮ Extensions of the classical theorems for very well-poised hypergeometric functions ⋮ Extension of some classical summation theorems for the generalized hypergeometric series with integral parameter differences ⋮ Unnamed Item ⋮ Generalizations of a formula due to Kummer with applications ⋮ NEW SERIES IDENTITIES FOR ${\frac{1}{\Pi}}$

Cites Work

• Unnamed Item
• Unnamed Item
• Contiguous extensions of Dixon's theorem on the sum of a \(_3F_2\)
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• A correction to some invariant imbedding equation of transport theory obtained by 'particle counting'
• Generalization of Kummer’s second theorem with applications
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• A summation formula for Clausen's series₃F₂(1) with an application to Goursat's function₂F₂(x)
• Comment on ‘A summation formula for Clausen's series₃F₂(1) with an application to Goursat's function₂F₂(x)’

This page was built for publication: Extensions of certain classical summation theorems for the series \(_2F_1\), \(_3F_2\) and with applications in Ramanujan's summations