Results 1 to 10 of about 2,005 (116)
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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Four Variants of Riemann Zeta Function
Mathematics, 2022 By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
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BPS indices, modularity and perturbations in quantum K-theory
Journal of High Energy Physics, 2022 We study a perturbation family of N $$ \mathcal{N} $$ = 2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians.
Hans Jockers +3 more
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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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A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds [PDF]
, 2018 We examine instances of modularity of (rigid) Calabi-Yau manifolds whose periods are expressed in terms of hypergeometric functions. The $p$-th coefficients $a(p)$ of the corresponding modular form can be often read off, at least conjecturally, from the ...
Zudilin, Wadim
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Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlev\'e IV Equation [PDF]
, 2014 We consider a $q$-Painlev\'e IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them
Nakazono, Nobutaka
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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.
CHU, Wenchang, BERNDT B. C.
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