A note on a further extension of Gauss’s second summation theorem with an application to the extension of two well-known combinatorial identities

DOI10.2989/16073606.2021.1925368OpenAlexW3166878113MaRDI QIDQ5089992

Gradimir V. Milovanović, In-Suk Kim, Arjun K. Rathie, Richard B. Paris

Publication date: 15 July 2022

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2989/16073606.2021.1925368

zbMATH Keywords

Gauss second summation theoremKnuth's old sumhypergeometric summation formulas and identitiesReed Dawson identityRiordan identity

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Generalized hypergeometric series, ({}_pF_q) (33C20) Applications of hypergeometric functions (33C90) Classical hypergeometric functions, ({}_2F_1) (33C05) Approximation to limiting values (summation of series, etc.) (40A25) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

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
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• Some summation theorems for generalized hypergeometric functions
• Generalizations of classical summation theorems for the series₂F₁and₃F₂with applications
• Applications of Basic Hypergeometric Functions
• 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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