Results 41 to 50 of about 135,153 (239)
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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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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Lattice paths and multiple basic hypergeometric series [PDF]
Pacific Journal of Mathematics, 1989 While each side of equations (0.1) and (0.2) is easily interpreted as a generating function for certain restricted partitions, the interpretation of the left-hand side of equation (0.3) presents more of a problem. It was William Burge [Bur 1, Bur 2] who demonstrated that the most natural interpretation is in terms of weighted binary words.
Agarwal, A. K., Bressoud, David M.
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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 ...
Arun Verma, Mizan Rahman
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Contiguous relations of hypergeometric series [PDF]
, 2003 The 15 Gauss contiguous relations for ${}_2F_1$ hypergeometric series imply that any three ${}_2F_1$ series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters).
Andrews +3 more
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Overpartition pairs and two classes of basic hypergeometric series [PDF]
, 2007 We study the combinatorics of two classes of basic hypergeometric series. We first show that these series are the generating functions for certain overpartition pairs defined by frequency conditions on the parts.
Lovejoy, Jeremy, Mallet, Olivier
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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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Transformation and reduction formulae for double q-Clausen series of type Φ1:1;μ1:2;λ [PDF]
, 2007 The Sears transformations are employed to establish several general series transformations for double q-Clausen hypergeometric series of type Φ1:1;μ1:2;λ.
Jia, Cangzhi, Wang, Tianming
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