Results 161 to 170 of about 6,972,539 (190)

A Quadratic Transformation of a Basic Hypergeometric Series

SIAM Journal on Mathematical Analysis, 1980
A quadratic transformation for a basic hypergeometric series is obtained.
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Summation Formulas for Basic Hypergeometric Series

SIAM Journal on Mathematical Analysis, 1981
Summation formulas for basic hypergeometric series are derived which are q-analogues of Minton’s [J. Math. Phys., 11 (1970), pp. 1375–1376] and Karlsson’s [J. Math. Phys., 12 (1971), pp. 270–271] summation formulas for generalized hypergeometric series, and some interesting limit cases are considered.
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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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Factors of a Kind of Truncated Basic Hypergeometric Series

Bulletin of the Malaysian Mathematical Sciences Society
The authors establish that a certain truncated basic hypergeometric series contains the factor \(\Phi_n(q)^2\), where \(\Phi_n(q)\) denotes the \(n\)th cyclotomic polynomial. This result extends and generalizes a recent theorem by \textit{J. Cao} et al. [Ramanujan J. 63, No. 4, 995--1005 (2024; Zbl 1536.33017)].
Su-Dan Wang
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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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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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Basic hypergeometric series

2004
George Gasper, Mizan Rahman
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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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Some New q-Congruences for Truncated Basic Hypergeometric Series: Even Powers

Results in Mathematics, 2020
Michael J Schlosser, Víctor J W Guo
exaly  

Basic Hypergeometric Series and Applications.

The American Mathematical Monthly, 1990
Ranjan Roy, Nathan J. Fine
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