Results 1 to 10 of about 66 (51)
On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications [PDF]
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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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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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 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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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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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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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 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 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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