Results 11 to 20 of about 1,933 (161)
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 ...
Eric T. Mortenson
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An asymptotic formula of the divergent bilateral basic hypergeometric series
, 2012 We show an asymptotic formula of the divergent bilateral basic hypergeometric series ${}_1 _0 (a;-;q,\cdot)$ with using the $q$-Borel-Laplace method. We also give the limit $q\to 1-0$ of our asymptotic formula.
Takeshi Morita
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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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Evaluation of beta integrals of Ramanujan type and integral representations for bilateral hypergeometric series [PDF]
The 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.
Howard S. Cohl, Hans Volkmer
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General Transformations of Bilateral Cognate Trigonometrical Series of Ordinary Hypergeometric Type [PDF]
Canadian Journal of Mathematics, 1953 Whipple [6] was the first to consider transformations connecting well-poised hypergeometric series as particular cases of relations between cognate trigonometrical series. He used contour integrals of the Barnes type to deduce such transformations. Later Sears [3] gave a systematic
Ravi P. Agarwal
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Certain Transformations of Nearly-Poised Bilateral Hypergeometric Series of Special Type [PDF]
Canadian Journal of Mathematics, 1958 A few years ago Bailey (1) gave certain transformations of both terminating and non-terminating nearly-poised hypergeometric series of the ordinary type and later on he also deduced basic analogues of some of his transformations.
H. S. Shukla
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Some more semi-finite forms of bilateral basic hypergeometric series
, 2005 9 ...
Frédéric Jouhet
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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.
Hjalmar Rosengren
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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.
Chuanan Wei, Tong Yu
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