Results 21 to 30 of about 133,643 (206)
A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
Mathematics, 2021 Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of ...
Hari Mohan Srivastava, Sama Arjika
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Multiple big q-Jacobi polynomials [PDF]
Bulletin of Mathematical Sciences, 2020 Here, we investigate type II multiple big q-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order q-difference equation, and we obtain ...
Fethi Bouzeffour, Mubariz Garayev
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$n$-color overpartitions, lattice paths, and multiple basic hypergeometric series [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We define two classes of multiple basic hypergeometric series $V_{k,t}(a,q)$ and $W_{k,t}(a,q)$ which generalize multiple series studied by Agarwal, Andrews, and Bressoud.
Olivier Mallet
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New double-sum expansions for certain Mock theta functions
AIMS Mathematics, 2022 The study of expansions of certain mock theta functions in special functions theory has a long and quite significant history. Motivated by recent correlations between q-series and mock theta functions, we establish a new q-series transformation formula ...
Qiuxia Hu +3 more
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Some q-Supercongruences from Transformation Formulas for Basic Hypergeometric Series [PDF]
Constructive approximation, 2018 Several new q -supercongruences are obtained using transformation formulas for basic hypergeometric series, together with various techniques such as suitably combining terms, and creative microscoping, a method recently developed by the first author in ...
Victor J. W. Guo, M. Schlosser
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Certain Transformation and Summation Formulae for Poly - Basic Hypergeometric Series
International Journal of Science and Research (IJSR), 2021 : We offer an overview of some of the main findings from the hypergeometric sequence theories and integrals associated with root systems. In particular, for such multiple series and integrals, we list a number of summations, transformations and explicit ...
Brijesh Pratap Singh
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The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results
Mathematics, 2021 The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is
Alexander Apelblat +2 more
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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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Several transformation formulas for basic hypergeometric series [PDF]
Journal of Difference Equations and Applications, 2021 In 1981, Andrews gave a four-variable generalization of Ramanujan's ${_1 _1}$ summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two ${_8 _7}$ series and Bailey's transformation formula for three ${_8 _7}$ series.
Chuanan Wei, Dianxuan Gong
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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.
R Agarwal, Arun Verma
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