Results 181 to 190 of about 5,104 (194)

q-Derivative Operators and Basic Hypergeometric Series

Results in Mathematics, 2006
By means of q-derivative operators, we investigate formal power series expansions. Two main expansion formulae in terms of q-derivative operators are established which can be considered as extensions of the corresponding results due to Carlitz (1973) and Liu (2002).
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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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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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Basic almost-poised hypergeometric series

Memoirs of the American Mathematical Society, 1998
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