Results 11 to 20 of about 38,611 (276)
Bilinear Identity for q-Hypergeometric Integrals [PDF]
, 1998 We describe a bilinear identity satisfied by certain multidimensional q-hypergeometric integrals. The identity can be considered as a deformation of the Riemann bilinear relation for the twisted de Rham (co)homologies.
Tarasov, Vitaly
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Rational Hypergeometric Identities [PDF]
Functional Analysis and Its Applications, 2021 6 pages, published ...
Gor Sarkissian, V. P. Spiridonov
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Hypergeometric evaluation identities and supercongruences [PDF]
Pacific Journal of Mathematics, 2009 In this article, we provide an application of hypergeometric evaluation identities, including a strange valuation of Gosper, to prove several supercongruences related to special valuations of truncated hypergeometric series. In particular, we prove a conjecture of van Hamme.
Линг Лонг
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Combinatorial Identities and Hypergeometric Functions, II [PDF]
Discrete Mathematics LettersSummary: Properties of the classical Gaussian hypergeometric function are applied to prove some combinatorial identities. Among others, a corrected and simplified version of a formula of \textit{D. Lim} [Notes Number Theory Discrete Math. 29, No. 3, 421--425 (2023; \url{doi:10.7546/nntdm.2023.29.3.421-425})] is offered. For Part I see [\textit{H. Alzer}
Horst Alzer
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Inversion Techniques and Combinatorial Identities: Balanced Hypergeometric Series [PDF]
Rocky Mountain Journal of Mathematics, 2002 After constructing the duplicate form of the Gould-Hsu inversion theorem, the author applies it to the derivation of summation theorems for terminating hypergeometric series with variable unity. The first type to be considered is \[ {_{5}F_{4}}\left[ \begin{matrix} -\delta -2n,\,a+x+n,\,b+x,\,z,\,\frac{1}{2}+x-z; \\ d+2z,e+2x-2z,\frac{1}{2}\left( c+x-n\
Wenchang Chu
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Bijective proofs of basic hypergeometric series identities [PDF]
Pacific Journal of Mathematics, 1987 The authors give simple, completely bijective proofs of the \(q\)-binomial theorem and Heine's \({}_2\Phi_1\) transformation. Since all identities on basic hypergeometric series can be built out of these two fundamental identities, any basic hypergeometric identity can be proved bijectively, at least in theory, by building bijections out of these ...
J. T. Joichi, Dennis Stanton
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Summation identities and transformations for hypergeometric series [PDF]
Annales mathématiques du Québec, 2017 We find summation identities and transformations for the McCarthy's $p$-adic hypergeometric series by evaluating certain Gauss sums which appear while counting points on the family $$Z_ : x_1^d+x_2^d=d x_1x_2^{d-1}$$ over a finite field $\mathbb{F}_p$. A.
Rupam Barman, Neelam Saikia
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Differentiation identities for hypergeometric functions
Expositiones Mathematicae, 2022 It is well-known that differentiation of hypergeometric function multiplied by a certain power function yields another hypergeometric function with a different set of parameters. Such differentiation identities for hypergeometric functions have been used widely in various fields of applied mathematics and natural sciences.
Hayato Motohashi
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Supercongruences arising from hypergeometric series identities [PDF]
Acta Arithmetica, 2018 By using some hypergeometric series identities, we prove two supercongruences on truncated hypergeometric series, one of which is related to a modular Calabi--Yau threefold, and the other is regarded as $p$-adic analogue of an identity due to Ramanujan.
Ji-Cai Liu
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Integral inequalities via harmonically h-convexity
Moroccan Journal of Pure and Applied Analysis, 2021 In this paper, we establish some estimates of the left side of the generalized Gauss-Jacobi quadrature formula for harmonic h-preinvex functions involving Euler’s beta and hypergeometric functions.
Merad Meriem +2 more
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