Results 11 to 20 of about 5,104 (194)
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. Our method can be applied to derive Ramanujan’s 1 ψ 1
William Y. C. Chen, Amy M. Fu
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Extension of the q-Pfaff-Saalschütz Theorem by Two Integer Parameters
Mathematics, 2022 We investigate a class of terminating 3ϕ2-series that comes from the balanced series perturbed by two extra integer parameters. By making use of the linearization method, a general summation formula is established that extends the well-known q-Pfaff ...
Nadia N. Li, Wenchang Chu
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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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New q-supercongruences arising from a summation of basic hypergeometric series
AIMS Mathematics, 2022 With the help of a summation of basic hypergeometric series, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we prove some new q-supercongruences on sums of q-shifted ...
Chuanan Wei, Chun Li
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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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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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