Results 11 to 20 of about 133,643 (206)
New q-supercongruences arising from a summation of basic hypergeometric series [PDF]
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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Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]
Symmetry, 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 multivariable extensions of the terminating very-well-poised 6-phi-5 summation formula.
Michael J. Schlosser
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Multilateral inversion of A_r, C_r and D_r basic hypergeometric series
, 2006 In [Electron. J. Combin. 10 (2003), #R10], the author presented a new basic hypergeometric matrix inverse with applications to bilateral basic hypergeometric series.
D.M. Bressoud +22 more
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Expansions of averaged truncations of basic hypergeometric series [PDF]
Proceedings 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 results for averages involving truncations of selected, more general, basic hypergeometric series. In
Schlosser, Michael, Zhou, Nian Hong
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Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems [PDF]
Encyclopedia of Special Functions: The Askey-Bateman Project, 2020 39 pages; small changes and references added; this text will appear as a chapter in the book "Multivariable Special Functions" (edited by Tom Koornwinder and Jasper Stokman) which is part of the new Askey-Bateman ...
M. Schlosser
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Factors of some truncated basic hypergeometric series [PDF]
Journal of Mathematical Analysis and Applications, 2019 We prove that certain basic hypergeometric series truncated at $k=n-1$ have the factor $ _n(q)^2$, where $ _n(q)$ is the $n$-th cyclotomic polynomial. This confirms two recent conjectures of the author and Zudilin. We also put forward some conjectures on $q$-congruences modulo $ _n(q)^2$.
Victor J. W. Guo
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Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers. [PDF]
Results 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.
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An affine Weyl group action on the basic hypergeometric series arising from the q-Garnier system [PDF]
Letters in Mathematical Physics, 2022 Recently, we formulated the q-Garnier system in a framework of an extended affine Weyl group of type A2n+1(1)×A1(1)×A1(1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}
Taiki Idomoto, Takao Suzuki
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Cyclotomic valuation of $q$-Pochhammer symbols and $q$-integrality of basic hypergeometric series [PDF]
Acta Arithmetica, 2022 We give a formula for the cyclotomic valuation of $q$-Pochhammer symbols in terms of (generalized) Dwork maps. We also obtain a criterion for the $q$-integrality of basic hypergeometric series in terms of certain step functions, which generalize Christol
B. Adamczewski +3 more
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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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