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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.
Chen, William Y. C., Fu, Amy M.
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Elementary derivations of identities for bilateral basic hypergeometric series [PDF]
Selecta Mathematica, 2000 We give elementary derivations of several classical and some new summation and transformation formulae for bilateral basic hypergeometric series. For purpose of motivation, we review our previous simple proof ("A simple proof of Bailey's very-well-poised
Schlosser, M.
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Ramanujan's radial limits and mixed mock modular bilateral q-hypergeometric series [PDF]
Proceedings of the Edinburgh Mathematical Society, 2016 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 ...
Mortenson, E.
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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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A bilateral series involving basic hypergeometric functions [PDF]
, 2003 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.
Hjalmar Rosengren
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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.
Aditya Agnihotri
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Several transformation formulas involving bilateral basic hypergeometric series [PDF]
, 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.
Chuanan Wei, Tong Yu
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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.
Bruce C. Berndt, Wenchang Chu
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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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The generalized Zwegers' $μ$-function and transformation formulas for the bilateral basic hypergeometric series [PDF]
, 2023 23 ...
Genki Shibukawa, Satoshi Tsuchimi
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