Results 11 to 20 of about 38,229 (306)
On a hypergeometric identity of Gelfand, Graev and Retakh [PDF]
Journal of Computational and Applied Mathematics, 2003 A hypergeometric identity equating a triple sum to a single sum, originally found by Gelfand, Graev and Retakh [Russian Math. Surveys 47 (1992), 1-88] by using systems of differential equations, is given hypergeometric proofs. As a bonus, several $q$-analogues can be derived.
Christian Krattenthaler +1 more
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A remarkable basic hypergeometric identity. [PDF]
Ramanujan JAbstract We give a closed form for quotients of truncated basic hypergeometric series where the base q is evaluated at roots of unity.
Krattenthaler C, Zudilin W.
europepmc +8 more sources
Hypergeometric evaluation identities and supercongruences [PDF]
Pacific Journal of Mathematics, 2011 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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Some applications of a hypergeometric identity [PDF]
Mathematical Sciences, 2015 In this paper, we use a general identity for generalized hypergeometric series to obtain some new applications. The first application is a hypergeometric-type decomposition formula for elementary special functions and the second one is a generalization of the well-known Euler identity \(e^{i\,x} = \cos x + i\,\sin x\) and an extension of hyperbolic ...
M.R. Eslahchi, Mohammad Masjed‐Jamei
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Hypergeometric Series and Harmonic Number Identities
Advances in Applied Mathematics, 2004 10 ...
Wenchang Chu, Livia De Donno
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Some properties of generalized hypergeometric Appell polynomials [PDF]
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $x^{(n)}$ denotes the Pochhammer symbol (rising factorial) defined by the formulas $x^{(0)}=1$ and $x^{(n)}=x(x+1)(x+2)\cdots (x+n-1)$ for $n\geq 1$.
L. Bedratyuk, N. Luno
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A New Identity for Generalized Hypergeometric Functions and Applications [PDF]
Axioms, 2019 We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published paper (
Mohammad Masjed-Jamei, Wolfram Koepf
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Bilinear Identity for q-Hypergeometric Integrals [PDF]
Osaka Journal of Mathematics, 1997 18 pages, amstex.tex (ver.
Tarasov, Vitaly
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Bailey pairs for the q-hypergeometric integral pentagon identity
European Physical Journal C: Particles and Fields, 2023 In this work, we construct new Bailey pairs for the integral pentagon identity in terms of q-hypergeometric functions. The pentagon identity considered here represents the equality of the partition functions of certain three-dimensional supersymmetric ...
Ilmar Gahramanov, Osman Erkan Kaluc
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Recurrent identities for two special functions of hypergeometric type
Вестник Самарского университета: Естественнонаучная серия, 2023 The article presents conclusions and proofs of Gauss-type identities for two known hypergeometric type functions. For the derivation and justification of formulas, the representation of functions in the form of a series is used, as well as an integral ...
Svetlana V. Podkletnova
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