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Expansions of averaged truncations of basic hypergeometric series [PDF]

open access: greenProceedings of the American Mathematical Society, 2023
Motivated by recent work of George Andrews and Mircea Merca [J. Combin. Theory Ser. A 119 (2012), pp. 1639–1643] on the expansion of the quotient of the truncation of Euler’s pentagonal number series by the complete series, we provide similar expansion ...
M. Schlosser, N. Zhou
semanticscholar   +5 more sources

The Cauchy operator for basic hypergeometric series [PDF]

open access: greenAdvances in Applied Mathematics, 2007
21 pages, to appear in Advances in Applied ...
Vincent Y. B. Chen, Nancy S. S. Gu
core   +9 more sources

New q-supercongruences arising from a summation of basic hypergeometric series [PDF]

open access: yesAIMS 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
doaj   +2 more sources

Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers. [PDF]

open access: yesResults Math, 2020
We provide several new q-congruences for truncated basic hypergeometric series with the base being an even power of q. Our results mainly concern congruences modulo the square or the cube of a cyclotomic polynomial and complement corresponding ones of an
Guo VJW, Schlosser MJ.
europepmc   +3 more sources

Associated Basic Hypergeometric Series [PDF]

open access: bronzeProceedings of the Glasgow Mathematical Association, 1953
The purpose of the present note is to give some interesting and simple identities connected with basic hypergeometric series of the types 2Φ1 and 3Φ2.
Ravi P. Agarwal
openalex   +3 more sources

Inversion of Bilateral Basic Hypergeometric Series [PDF]

open access: bronzeThe 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.
Michael J. Schlosser
openalex   +5 more sources

Transformation formulae for multivariable basic hypergeometric series [PDF]

open access: greenMethods and Applications of Analysis, 1998
Latex2e, 17 ...
T. H. Baker, Peter J. Forrester
openalex   +4 more sources

Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]

open access: yesSymmetry, Integrability and Geometry: Methods and Applications, 2007
We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent ...
Michael J. Schlosser
doaj   +5 more sources

Particle seas and basic hypergeometric series

open access: bronzeAdvances in Applied Mathematics, 2003
AbstractParticle seas were introduced by Claude Itzykson to give a direct combinatorial proof of the Jacobi triple product [Viennot, Empilements, 1999]. We show here how generalized particle seas can be employed to give bijective proofs of several identities in the theory of basic hypergeometric series.
Sylvie Corteel
openalex   +2 more sources

Generalized basic hypergeometric series with unconnected bases (II)’ [PDF]

open access: bronzeThe Quarterly Journal of Mathematics, 1970
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.
Ravi P. Agarwal, Arun Verma
openalex   +4 more sources

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