Results 1 to 10 of about 1,933 (161)
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 Ramanujanβs 1 Ο 1
William Y. C. Chen, Amy M. Fu
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Elementary derivations of identities for bilateral basic hypergeometric series [PDF]
Selecta Mathematica, 2003 LaTeX2e, 35 pages, revised abstract and ...
Michael J. Schlosser
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On a New Summation Formula for πππ Basic Bilateral Hypergeometric Series and Its Applications [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2π2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, π-gamma, and π-beta function identities.
D. D. Somashekara +2 more
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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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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.
Michael J. Schlosser
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Bilateral inversions and terminating basic hypergeometric series identities
Discrete Mathematics, 2008 AbstractThe q-analogue of Legendre inversions 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 3Ο2-series, well-poised 8Ο7-series and bilateral 6Ο6-series.
Wenchang Chu, Chenying Wang
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Two entries on bilateral hypergeometric series in Ramanujan's lost notebook [PDF]
Proceedings of the American Mathematical Society, 2006 Two entries of bilateral sums in Ramanujan's lost notebook are confirmed by means of Dougall's bilateral series identities with one of them being corrected.
Bruce C. Berndt, Wenchang Chu
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On certain relations between products of bilateral hypergeometric series [PDF]
Proceedings of the Glasgow Mathematical Association, 1957 Darling [3] in 1932 and Bailey [2] in 1933 gave certain theorems on products of hypergeometric series. Again in 1948 Sears [4] used the relation which expresses the series in terms of M other series of the same type to derive transformations between products of both basic and ordinary hypergeometric series. In this paper I give certain general theorems
Harishanker Shukla
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On a β2-valued integral index transform and bilateral hypergeometric series [PDF]
Integral Transforms and Special Functions, 2022 We discuss the spectral decomposition of the hypergeometric differential operators on the line Rez=1/2, such operators arise in the problem of decomposition of tensor products of unitary representations of the universal covering of the group SL(2,R). Our main purpose is a search of natural bases in generalized eigenspaces and variants of the inversion ...
Yury A. Neretin
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On certain transformations of poly-basic bilateral hypergeometric series
Journal of Computational and Applied Mathematics, 2003 AbstractIn this paper, we have established certain transformations of basic hypergeometric series with more than one base. Some of these lead to the relationship between product of two q-series. These results, in turn, lead to very interesting transformations of bi-basic and poly-basic q-series. A few of the results which are representative of the many
R. Y. Denis, S. N. Singh, Satya P. Singh
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