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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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Some relations on Humbert matrix polynomials [PDF]
Mathematica Bohemica, 2016 The Humbert matrix polynomials were first studied by Khammash and Shehata (2012). Our goal is to derive some of their basic relations involving the Humbert matrix polynomials and then study several generating matrix functions, hypergeometric matrix ...
Ayman Shehata
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An extension to overpartitions of Rogers-Ramanujan identities for even moduli [PDF]
Discrete Mathematics & Theoretical Computer Science, 2006 We investigate class of well-poised basic hypergeometric series $\tilde{J}_{k,i}(a;x;q)$, interpreting these series as generating functions for overpartitions defined by multiplicity conditions.
Sylvie Corteel +2 more
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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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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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Summation Formulae for Quintic q-Series
Mathematics, 2022 By utilizing the modified Abel lemma on summation by parts, we examine a class of quintic q-series, that have close connections to the “twisted cubic q-series”. Several remarkable summation and transformation formulae are established.
Wenchang Chu
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The Askey–Wilson Integral and Extensions
Mathematics, 2023 By means of the q-derivative operator method, we review the q-beta integrals of Askey–Wilson and Nassrallah–Rahman. More integrals are evaluated by the author, making use of Bailey’s identity of well-poised bilateral 6ψ6-series as well as the extended ...
Wenchang Chu
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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 ϕ 1 _2{\phi _1} and very-well-poised 8 ϕ 7 _8{\phi _7} basic ...
Rahman, Mizan, Verma, Arun
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On Convergence of q-Series Involving ϕr+1r Basic Hypergeometric Series
Journal of Inequalities and Applications, 2009 We use inequality technique and the terminating case of the q-binomial formula to give some results on convergence of q-series involving ϕr+1r basic hypergeometric series.
Mingjin Wang, Xilai Zhao
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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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