Results 11 to 20 of about 584 (125)

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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A Bilateral Series Involving Basic Hypergeometric Functions [PDF]

, 2005
We prove a summation formula for a bilateral series whose terms are products of two basic hypergeometric functions. In special cases, series of this type arise as matrix elements of quantum group representations.
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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.
CHU, Wenchang, WANG C.
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Ramanujan's Radial Limits and Mixed Mock Modular Bilateralq-Hypergeometric Series [PDF]

Proceedings of the Edinburgh Mathematical Society, 2015
AbstractUsing results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsomet al.for mock theta functions. Here we see that Mortenson's previous work on the dual nature of Appell–Lerch sums and partial theta functions and on constructing bilateralq-series with mixed mock modular behaviour is well ...
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New Mock Theta Function Identities via Fractional q-Calculus and Bilateral ₂ψ₂ Series

Fractal and Fractional
Mock theta functions, introduced by Ramanujan in his last letter to Hardy, play a significant role in q-series theory and have natural connections to fractional q-calculus. In this paper, we study bilateral hypergeometric series of the form ψ22= ∑n=−∞∞(a,
Qiuxia Hu, Bilal Khan
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Elementary derivations of identities for bilateral basic hypergeometric series [PDF]

Selecta Mathematica, 2003
LaTeX2e, 35 pages, revised abstract and ...
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Several transformation formulas involving bilateral basic hypergeometric series

, 2019
In terms of the analytic continuation method, we prove three transformation formulas involving bilateral basic hypergeometric series. One of them is equivalent to Jouhet's result involving two $_8 _8$ series and two $_8 _7$ series.
Wei, Chuanan, Yu, Tong
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Bilateral Basic Hypergeometric Series: A Study

Anusandhaan - Vigyaan Shodh Patrika, 2018
In the present work, certain transformations and summation formulae for basic bilateral hypergeometric series have been discussed. This study also gives the method of obtaining new transformations and summation formulae for basic bilateral hypergeometric series. Some of the applications have been mentioned.
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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
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On a ℂ²-valued integral index transform and bilateral hypergeometric series

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 ...
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