Results 11 to 20 of about 135,153 (239)
Semi-Finite Forms of Bilateral Basic Hypergeometric Series [PDF]
Proceedings of the American Mathematical Society, 2005 We show that several classical bilateral summation and transformation formulas have semi-finite forms. We obtain these semi-finite forms from unilateral summation and transformation formulas. Our method can be applied to derive Ramanujan’s 1 ψ 1
William Y. C. Chen, Amy M. Fu
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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
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$n$-color overpartitions, lattice paths, and multiple basic hypergeometric series [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We define two classes of multiple basic hypergeometric series $V_{k,t}(a,q)$ and $W_{k,t}(a,q)$ which generalize multiple series studied by Agarwal, Andrews, and Bressoud.
Olivier Mallet
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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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The contiguous function relations for the basic hypergeometric series
Journal of Mathematical Analysis and Applications, 1990 De facon analogue aux developpements de Rainville de relations contigues pour la fonction hypergeometrique generalisee on etablit ce type de relations pour la q-extension de cette fonction, la fonction hypergeometrique de base.
René F. Swarttouw
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Mock Jacobi forms in basic hypergeometric series [PDF]
Compositio Mathematica, 2009 AbstractWe show that someq-series such as universal mock theta functions are linear sums of theta quotients and mock Jacobi forms of weight 1/2, which become holomorphic parts of real analytic modular forms when they are restricted to torsion points and multiplied by suitable powers ofq.
Andrews +4 more
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Parameter Augmentation for Basic Hypergeometric Series, II
Journal of Combinatorial Theory, Series A, 1997 AbstractIn a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-summation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation forq-integrals such as the Askey–Wilson ...
William Y. C. Chen, Zhiguo Liu
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Certain Transformation and Summation Formulae for Poly - Basic Hypergeometric Series
International Journal of Science and Research (IJSR), 2021 : We offer an overview of some of the main findings from the hypergeometric sequence theories and integrals associated with root systems. In particular, for such multiple series and integrals, we list a number of summations, transformations and explicit ...
Brijesh Pratap Singh
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Elementary derivations of identities for bilateral basic hypergeometric series [PDF]
Selecta Mathematica, 2003 LaTeX2e, 35 pages, revised abstract and ...
Schlosser, M.
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Several transformation formulas for basic hypergeometric series [PDF]
Journal of Difference Equations and Applications, 2021 In 1981, Andrews gave a four-variable generalization of Ramanujan's ${_1 _1}$ summation formula. We establish a six-variable generalization of Andrews' identity according to the transformation formula for two ${_8 _7}$ series and Bailey's transformation formula for three ${_8 _7}$ series.
Chuanan Wei, Dianxuan Gong
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