Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters

DOI10.1090/S0025-5718-2011-02512-3zbMath1236.33013OpenAlexW1978439009MaRDI QIDQ3117219

Chu, Wenchang

Publication date: 17 February 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2011-02512-3

zbMATH Keywords

classical hypergeometric seriesDixon's theoremWatson's formulaDougall's theorem for well-poised seriesthe Thomae transformationWhipple's formula

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (34)

Terminating \(q\)-Whipple summation theorem with two integer parameters ⋮ The Clausenian hypergeometric function \({}_3 F_2\) with unit argument and negative integral parameter differences ⋮ Unnamed Item ⋮ Terminating ₂𝐹₁(4)-series perturbed by two integer parameters ⋮ Unnamed Item ⋮ The arithmetic Kuznetsov formula on \(\mathrm{GL}(3)\). II: The general case ⋮ Another class of nonterminating \(_3F_2\)-series with a free argument ⋮ Evaluation of nonterminating \(_3F_2(\frac{1}{4})\)-series perturbed by three integer parameters ⋮ Infinite series involving harmonic numbers of convergence rate 1/2 ⋮ Summation formulae for \(q\)-Watson type \(4\phi 3\)-series ⋮ Terminating balanced $_4\phi _3$-series with two integer parameters ⋮ TERMINATING ALMOST POISED <i>q</i>-DIXON SUMS ⋮ Transformation formulae for terminating balanced $_4F_3$-series and implications ⋮ Contiguous values for a class of nonterminating ₃F₂(1)-series ⋮ Infinite series around multinomial coefficients and harmonic numbers ⋮ Expansions over Legendre polynomials and infinite double series identities ⋮ Nonterminating ₃F₂-series with a free variable ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Variations on a hypergeometric theme ⋮ Non-terminating₃F₂-series with unit argument ⋮ Binomial sums involving Catalan numbers ⋮ Unnamed Item ⋮ Loop equation analysis of the circular \(\beta\) ensembles ⋮ Terminating ₃F₂(4)-series extended with three integer parameters ⋮ Harmonic sums from the Kummer theorem ⋮ Lemniscate-like constants and infinite series ⋮ Terminating balanced \(_{4}F_{3}\)-series and very well-poised \(_{7}F_{6}\)-series ⋮ Terminating balanced \({}_4\phi_3\)-series and very well-poised \({}_8\phi_7\)-series ⋮ Further Ramanujan-like series containing harmonic numbers and squared binomial coefficients ⋮ Terminating₄F₃-series extended with two integer parameters ⋮ Some summation theorems for Clausen's hypergeometric functions with unit argument ⋮ Alternating convolutions of Catalan numbers ⋮ EVALUATION OF CERTAIN EXOTIC (1)-SERIES

Cites Work

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• Irreducible recurrences and representation theorems for \(_ 3F_ 2(1)\)
• Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\)
• Generalized Watson's summation formula for \(_3F_2(1)\)
• Generalizations of Whipple's theorem on the sum of a \({}_ 3 F_ 2\)
• A study of new hypergeometric transformations
• Some Summation Formulas for the Series 3 F 2 (1)
• Generalizations of Dixon's Theorem on the Sum of A 3 F 2
• ON PREECE'S IDENTITY AND OTHER CONTIGUOUS RESULTS
• A SUMMATION FORMULA OF₆F₅(1)
• A Generalization of the Theorems of Watson and Whipple on the Sum of the Series ₃ F ₂

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