Results 31 to 40 of about 133,643 (206)
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
doaj +1 more source
Inversion of Bilateral Basic Hypergeometric Series [PDF]
The Electronic Journal of Combinatorics, 2003 We present a new matrix inverse with applications in the theory of bilateral basic hypergeometric series. Our matrix inversion result is directly extracted from an instance of Bailey's very-well-poised ${}_6\psi_6$ summation theorem, and involves two infinite matrices which are not lower-triangular.
openaire +4 more sources
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.
openaire +3 more sources
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
doaj +1 more source
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
doaj +1 more source
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
openaire +2 more sources
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
doaj +1 more source
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
core +3 more sources
Some New q-Congruences for Truncated Basic Hypergeometric Series [PDF]
Symmetry, 2019 We provide several new q-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric generalizations thereof.
Victor J. W. Guo, M. Schlosser
semanticscholar +1 more source
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
core +1 more source