Results 1 to 10 of about 564 (105)
Application of the residue theorem to bilateral hypergeometric series
Le Matematiche, 2007 The application of the residue theorem to bilateral hypergeometric series identities is systematically reviewed by exemplifying three classes of summation theorems due to Dougall (1907), Jackson (1949, 1952) and Slater-Lakin (1953).
Wenchang Chu, Xiaoxia Wang, Deyin Zheng
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Four Variants of Riemann Zeta Function
Mathematics, 2022 By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
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Semi-finite forms of bilateral basic hypergeometric series [PDF]
Proceedings of the American Mathematical Society, 2005 We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s 1 ψ 1
Chen, William Y. C., Fu, Amy M.
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BPS indices, modularity and perturbations in quantum K-theory
Journal of High Energy Physics, 2022 We study a perturbation family of N $$ \mathcal{N} $$ = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians.
Hans Jockers +3 more
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Inversion of Bilateral Basic Hypergeometric Series [PDF]
The Electronic Journal of Combinatorics, 2003 We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular.
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Two entries on bilateral hypergeometric series in Ramanujan's lost notebook [PDF]
Proceedings of the American Mathematical Society, 2006 The authors confirm two results on bilateral hypergeometric series presented on page 200 of Ramanujan's lost notebook, with one of them being corrected. The proof of the second formula is based on Dougall's bilateral series identities.
CHU, Wenchang, BERNDT B. C.
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New Curious Bilateral q-Series Identities
Axioms, 2012 By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived.
Frédéric Jouhet, Michael J. Schlosser
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On generalization of continued fraction of Gauss
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
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ON BILATERAL BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS
International Journal of Apllied Mathematics, 2013 Summary: This article deals with the derivation of continued fraction involving bilateral basic hypergeometric series by making use of known three term relations and other known results of R. P. Agarwal.
Srivastava, Pankaj +1 more
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On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications
International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2𝜓2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, 𝑞-gamma, and 𝑞-beta function identities.
D. D. Somashekara +2 more
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