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The Cauchy Operator for Basic Hypergeometric Series [PDF]
Advances in Applied Mathematics, 2007 We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator ...
Chen, Vincent Y. B., Gu, Nancy S. S.
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Mock Jacobi forms in basic hypergeometric series [PDF]
Compositio Mathematica, 2008 We show that some $q$-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion points and ...
Andrews +4 more
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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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One-parameter orthogonality relations for basic hypergeometric series [PDF]
Indagationes Mathematicae, 2003 The second order hypergeometric q-difference operator is studied for the value c=-q. For certain parameter regimes the corresponding recurrence relation can be related to a symmetric operator on the Hilbert space l^2(Z).
Koelink, Erik
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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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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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Transformation formulas for multivariable basic hypergeometric series [PDF]
Methods and Applications of Analysis, 1999 Latex2e, 17 ...
T. H. Baker, P. J. Forrester
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Limits of elliptic hypergeometric biorthogonal functions [PDF]
, 2011 The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-Askey scheme of basic hypergeometric orthogonal polynomials.
Askey +15 more
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The c-function expansion of a basic hypergeometric function associated to root systems [PDF]
, 2014 We derive an explicit c-function expansion of a basic hypergeometric function associated to root systems. The basic hypergeometric function in question was constructed as explicit series expansion in symmetric Macdonald polynomials by Cherednik in case ...
Gasper +11 more
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