Gauss's \(_ 2F_ 1(1)\) cannot be generalized to \(_ 2F_ 1(x)\)

DOI10.1016/0377-0427(92)90211-FzbMath0764.33001OpenAlexW1984967714MaRDI QIDQ1196839

Doron Zeilberger

Publication date: 16 January 1993

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(92)90211-f

zbMATH Keywords

explicit evaluationclosed formWimp's theorem

Mathematics Subject Classification ID

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

Related Items (9)

Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I: Connection to the hypergeometric function \(_{3}F_{2}\) ⋮ A generalized inverse binomial summation theorem and some hypergeometric transformation formulas ⋮ Generalized Watson's summation formula for \(_3F_2(1)\) ⋮ A hypergeometric version of the modularity of rigid Calabi-Yau manifolds ⋮ M. Jackson's bilateral \(_{3} H _{3}\)-series and extension with integer parameters ⋮ On Cauchy-Liouville-Mirimanoff polynomials. II ⋮ A generalization of Euler’s hypergeometric transformation ⋮ An Analytic Method for Convergence Acceleration of Certain Hypergeometric Series ⋮ Analytical formulae for extended $_{3}F_{2}$-series of Watson–Whipple–Dixon with two extra integer parameters

Cites Work

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• Irreducible recurrences and representation theorems for \(_ 3F_ 2(1)\)
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Strange Evaluations of Hypergeometric Series
• Generating Functions for Bessel and Related Polynomials

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