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Associated Basic Hypergeometric Series [PDF]
Proceedings of the Glasgow Mathematical Association, 1953 The purpose of the present note is to give some interesting and simple identities connected with basic hypergeometric series of the types 2Φ1 and 3Φ2.
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The Cauchy operator for basic hypergeometric series
Advances in Applied Mathematics, 2008 We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2ϕ_1$ transformation formula and Sears' ${}_3ϕ_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities.
Vincent Y. B. Chen, Nancy S. S. Gu
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GENERALIZED BASIC HYPERGEOMETRIC SERIES WITH UNCONNECTED BASES (II) [PDF]
The Quarterly Journal of Mathematics, 1967 In a series of recent papers Verma and Upadhyay (7,8,9) developed the theory of basic hypergeometric series with two bases q and q½. These investigations were made in an attempt to discover a summation formula for a bilateral basic hypergeometric series 2Ψ2 analogous to that for a 2H2 (cf.
Agarwal, R. P., Verma, A.
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Lattice paths and multiple basic hypergeometric series [PDF]
Pacific Journal of Mathematics, 1989 The equivalence between certain identities for basic hypergeometric series and some combinatorial identities for colored partitions is established by viewing the basic hypergeometric series as generating functions for weighted lattice paths.
Agarwal, A. K., Bressoud, David M.
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Some Remarks on Very-Well-Poised 8ϕ7 Series
Symmetry, Integrability and Geometry: Methods and Applications, 2012 Nonpolynomial basic hypergeometric eigenfunctions of the Askey-Wilson second order difference operator are known to be expressible as very-well-poised 8ϕ7 series.
Jasper V. Stokman
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Gottlieb Polynomials and Their q-Extensions
Mathematics, 2021 Since Gottlieb introduced and investigated the so-called Gottlieb polynomials in 1938, which are discrete orthogonal polynomials, many researchers have investigated these polynomials from diverse angles.
Esra ErkuŞ-Duman, Junesang Choi
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Transformation formulas for multivariable basic hypergeometric series [PDF]
Methods and Applications of Analysis, 1999 We study multivariable (bilateral) basic hypergeometric series associated with (type $A$) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's ${}_2ϕ_1$ transformation, the $q$-Pfaff-Kummer and Euler transformations, the $q$-Saalschütz summation formula and Sear's transformation
Baker, T. H., Forrester, P. J.
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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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Fractal and Fractional, 2023 In the geometric function theory of complex analysis, the investigation of the geometric properties of analytic functions using q-analogues of differential and integral operators is an important area of study, offering powerful tools for applications in ...
Suha B. Al-Shaikh +3 more
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Quadratic transformation formulas for basic hypergeometric series [PDF]
Transactions of the American Mathematical Society, 1993 Starting with some of the known transformation formulas for well-poised 2
Rahman, Mizan, Verma, Arun
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