Results 91 to 100 of about 5,521 (197)
Matrix q-hypergeometric series
, 1995 After extending the basic hypergeometric series to series with matrix coefficients, we apply them to the solution of q-difference-q-differential equations, and to the formulation of a versatile tool for producing generating functions and series-product ...
Yang, Kung-Wei
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, 2004 A multiple generalization of the Euler transformation formula for basic hypergeometric series 2φ1 is derived. It is obtained from the symmetry of the reproducing kernel for Macdonald polynomials by a method of multiple principal specialization.
Kajihara, Yasushi
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Overpartition pairs and two classes of basic hypergeometric series
, 2008 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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Combinatorial proofs of identities in basic hypergeometric series
European Journal of Combinatorics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Balanced3ϕ2Summation Theorems forU(n) Basic Hypergeometric Series
, 1997 In this paper we begin the theory and application of theU(n+1) generalization of the classical Bailey Transform and Bailey Lemma. We work in the setting of multiple basic hypergeometric series very-well-poised on unitary groupsU(n+1).
Milne, Stephen C.
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Plancherel–Rotach asymptotics for certain basic hypergeometric series
, 2008 In this work we study the chaotic and periodic asymptotics for the confluent basic hypergeometric series. For a fixed q∈(0,1), the asymptotics for Euler's q-exponential, q-Gamma function Γq(x), q-Airy function of K. Kajiwara, T. Masuda, M. Noumi, Y. Ohta
Zhang, Ruiming
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Some Theorems on Generalized Basic Hypergeometric Series
, 2014 In an earlier paper the author has established two theorems on generalized hypergeometric functions. In each theorem a numerator differs from a denominator by a positive integer.
Wadhwa, A. D.
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, 2023 We derive double product representations of nonterminating basic hypergeometric series using diagonalization, a method introduced by Theo William Chaundy in 1943.
Cohl, Howard S. +1 more
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An Upper Bound for a Basic Hypergeometric Series
, 1996 We show that if 0 x 2 q 1, then the basic hypergeometric series P n k=0 \Gamma n k \Delta q x k is bounded above by the product Q n\Gamma1 k=0 (1 + xq k=2 ).
Danny Krizanc +2 more
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