Karlsson–Minton summation theorems for the generalized hypergeometric series of unit argument

DOI10.1080/10652460903497259zbMath1200.33007OpenAlexW1966864447MaRDI QIDQ3584674

Publication date: 30 August 2010

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460903497259

zbMATH Keywords

gamma function combinatorial identities generalized hypergeometric series binomial coefficients Karlsson-Minton summation formul

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Gamma, beta and polygamma functions (33B15) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (21)

Clausen's series₃F₂(1) with integral parameter differences and transformations of the hypergeometric function₂F₂(x) ⋮ On extensions of two results due to Ramanujan ⋮ The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ Extensions of Karlsson–Minton summation theorem and some consequences of the first Miller–Paris transformation ⋮ Fractional integral operators characterized by some new hypergeometric summation formulas ⋮ An alternative proof of the extended Saalschütz summation theorem for the _{r + 3} F _{r + 2} (1) series with applications ⋮ Generalized hypergeometric identities with extra parameters ⋮ New identities for a sum of products of the Kummer functions ⋮ Some properties of a family of incomplete hypergeometric functions ⋮ A contiguous extension of Dixon’s theorem for a terminating 4F3(1) series with applications ⋮ Euler-type transformations for the generalized hypergeometric function \(_{r+2} F _{r+1}(x)\) ⋮ Transformation formulas for the generalized hypergeometric function with integral parameter differences ⋮ Some families of combinatorial and other series identities and their applications ⋮ Alternative Approach to Miller-Paris Transformations and Their Extensions ⋮ Certain transformations and summations for generalized hypergeometric series with integral parameter differences ⋮ Unnamed Item ⋮ Some summation theorems for generalized hypergeometric functions ⋮ Degenerate Miller-Paris transformations ⋮ 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 ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument

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