Results 171 to 180 of about 5,265 (203)

Some Summation Formulae for Nonterminating Basic Hypergeometric Series

SIAM Journal on Mathematical Analysis, 1985
Andrews found basic hypergeometric extensions of the Watson and Whipple \({}_ 3F_ 2\) sums in the terminating cases. His series were balanced \({}_ 4\phi_ 3's\). By Watson's transformation these can be written as very well poised \({}_ 8\phi_ 7's\). The authors obtain nonterminating extensions of these \({}_ 3F_ 2\) sums as very well poised \({}_ 8 ...
Verma, A., Jain, V. K.
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Certain Summation Formulae for Basic Hypergeometric Series

Canadian Mathematical Bulletin, 1977
In 1927, Jackson [5] obtained a transformation connecting awhere N is any integer, with aviz.,1where | q | > l and |qγ-α-βN| > l.
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Some q-supercongruences for truncated basic hypergeometric series

Acta Arithmetica, 2015
Summary: For any odd prime \(p\) we obtain \(q\)-analogues of van Hamme's and Rodriguez-Villegas' supercongruences involving products of three binomial coefficients such as \[ \begin{aligned} \sum_{k=0}^{{(p-1)}/{2}} \bigg[{2k\atop k}\bigg]_{q^2}^3 \frac{q^{2k}}{(-q^2;q^2)_k^2 (-q;q)_{2k}^2} &\equiv 0 \pmod{[p]^2} \;\text{for}\;p\equiv 3 \pmod 4 ...
Guo, Victor J.W., Zeng, Jiang
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On Certain Transformation Formulas Involving Basic Hypergeometric Series

Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Singh, Satya Prakash, Yadav, Vijay
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Some Basic Extensions of Gustafson-Rakha's Multivariate Basic Hypergeometric Series

Annals of Combinatorics, 2002
The author establishes that when \(m=2n\), and \(n=1\), one of the two multivariate basic hypergeometric series associated with the root system of classical Lie algebra obtained earlier by \textit{R. A. Gustafson} and the author [Ann. Comb. 4, 347-373 (2000; Zbl 0971.33009)] is equivalent to Jackson's \({}_8\psi_7\) sum while the other series is ...
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Remarks on Some Basic Hypergeometric Series

2005
Many results in Mathematical Analysis seem to come from some “obvious” computations. For a few years, we have been interested in the analytic theory of linear q-difference equations. One of the problems we are working on is the analytical classification of q-difference equations. Recall that this problem was already considered by G. D.
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment

Ca-A Cancer Journal for Clinicians, 2022
Jun J Mao,, Msce, Lorenzo Cohen, Karen M Mustian   +2 more
exaly  

Basic Hypergeometric Series and Applications.

The American Mathematical Monthly, 1990
Ranjan Roy, Nathan J. Fine
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WELL-POISED BASIC HYPERGEOMETRIC SERIES

The Quarterly Journal of Mathematics, 1947
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Obesity and adverse breast cancer risk and outcome: Mechanistic insights and strategies for intervention

Ca-A Cancer Journal for Clinicians, 2017
Cynthia Morata-Tarifa, Joyce M Slingerland   +1 more
exaly