Results 1 to 10 of about 135,153 (239)
Expansions of averaged truncations of basic hypergeometric series [PDF]
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]
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]
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]
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]
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]
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]
Latex2e, 17 ...
T. H. Baker, Peter J. Forrester
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Macdonald Polynomials and Multivariable Basic Hypergeometric Series [PDF]
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
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]
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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