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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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On a New Summation Formula for 𝟐𝜓𝟐 Basic Bilateral Hypergeometric Series and Its Applications [PDF]
International Journal of Mathematics and Mathematical Sciences, 2011 We have obtained a new summation formula for 2𝜓2 bilateral basic hypergeometric series by the method of parameter augmentation and demonstrated its various uses leading to some development of etafunctions, 𝑞-gamma, and 𝑞-beta function identities.
D. D. Somashekara +2 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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Duality relations for hypergeometric series [PDF]
, 2014 We explicitly give the relations between the hypergeometric solutions of the general hypergeometric equation and their duals, as well as similar relations for q-hypergeometric equations.
Beukers, Frits, Jouhet, Frédéric
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New Curious Bilateral q-Series Identities
Axioms, 2012 By applying a classical method, already employed by Cauchy, to a terminating curious summation by one of the authors, a new curious bilateral q-series identity is derived.
Frédéric Jouhet, Michael J. Schlosser
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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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ON BILATERAL BASIC HYPERGEOMETRIC SERIES AND CONTINUED FRACTIONS
International Journal of Apllied Mathematics, 2013 Summary: This article deals with the derivation of continued fraction involving bilateral basic hypergeometric series by making use of known three term relations and other known results of R. P. Agarwal.
Srivastava, Pankaj +1 more
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On generalization of continued fraction of Gauss
International Journal of Mathematics and Mathematical Sciences, 1990 In this paper we establish a continued fraction represetation for the ratio qf two basic bilateral hypergeometric series 2ψ2's which generalize Gauss' continued fraction for the ratio of two 2F1's.
Remy Y. Denis
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Rains, Eric M., van de Bult, Fokko J.
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