Results 1 to 10 of about 135,153 (239)
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 ...
M. Schlosser, N. Zhou
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The Cauchy operator for basic hypergeometric series [PDF]
Advances in Applied Mathematics, 2007 21 pages, to appear in Advances in Applied ...
Vincent Y. B. Chen, Nancy S. S. Gu
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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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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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Associated Basic Hypergeometric Series [PDF]
Proceedings 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
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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.
Michael J. Schlosser
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Transformation formulae for multivariable basic hypergeometric series [PDF]
Methods and Applications of Analysis, 1998 Latex2e, 17 ...
T. H. Baker, Peter J. Forrester
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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 ...
Michael J. Schlosser
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Particle seas and basic hypergeometric series
Advances 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
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Generalized basic hypergeometric series with unconnected bases (II)’ [PDF]
The 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
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