Results 1 to 10 of about 617 (115)
Bilateral inversions and terminating basic hypergeometric series identities
Discrete Mathematics, 2009 A \(q\)-analogue of the Legendre inversion is established and generalized to bilateral sequences. They are employed to investigate the dual relations of three basic formulae due to Jackson and Bailey, on balanced \(_{3}\phi_{2}\)-series, well-poised \(_{8}\phi_{7}\)-series and bilateral \(_{6}\psi_{6}\)-series.
Wenchang Chu, Chenying Wang
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On certain transformations of poly-basic bilateral hypergeometric series
Journal of Computational and Applied Mathematics, 2003 The authors establish transformations of poly-basic bilateral hypergeometric series in terms of another similar series not necessary having the same number of bases. As application of the obtained results, they derive expressions of the product of two \(q\)-series in terms of another product of two series which lead to interesting transformations of ...
Denis, Remy Y., Singh, S.N., Singh, S.P.
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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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Elementary derivations of identities for bilateral basic hypergeometric series [PDF]
Selecta Mathematica, New Series, 2003 LaTeX2e, 35 pages, revised abstract and ...
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On transformation of certain bilateral basic hypergeometric series and their applications
Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2019 In this paper, the authors presented transformation and summation formulae for bilateral basic hypergeometric series: \[\sum_{n=-\infty}^{\infty}\frac{(a)_n}{(b)_n}z^n= \frac{(b/a;q)_\infty}{(b,bz/a;q)_\infty}\sum_{n=-\infty}^{\infty}(a)_nz^n\] whenever \(\max\{|b/a|,|1/b|\}
D D Somashekara
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Ramanujan JournalAbstract In this paper we evaluate integrals of products of gamma functions of Ramanujan type in terms of bilateral hypergeometric series. In cases where the bilateral hypergeometric series are summable, then we evaluate these integral as beta integrals. In addition, we obtain integral representations for bilateral hypergeometric series.
Hans Volkmer +2 more
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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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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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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
Chen, William Y. C., Fu, Amy M.
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