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Summation Formulas for Basic Hypergeometric Series
SIAM Journal on Mathematical Analysis, 1981Summation 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 from squares of basic hypergeometric series
RACSAM, 2023Hanfei Song, Chun Wang
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q-Derivative Operators and Basic Hypergeometric Series
Results in Mathematics, 2006By 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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Indian journal of pure and applied mathematics, 2022
Zhizheng Zhang, Hanfei Song
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Zhizheng Zhang, Hanfei Song
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CERTAIN NEW IDENTITIES OF BASIC BILATERAL HYPERGEOMETRIC SERIES
South East Asian J. of Mathematics and Mathematical SciencesIn the present work, we have applied Cauchy’s method to establish some basic bilateral hypergeometric series identities, using the known identities of terminating unilateral series. We also have discussed some important special cases of our results.
S. A. Ali, Saloni Kushvaha
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Remarks on Some Basic Hypergeometric Series
2005Many 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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On Certain Transformation Formulas Involving Basic Hypergeometric Series
Proceedings of the National Academy of Sciences India Section A Physical Sciences, 2020S. Singh, V. Yadav
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Three-term relations for basic hypergeometric series
Journal of Mathematical Analysis and Applications, 2018Abstract Any three basic hypergeometric series ϕ 1 2 whose respective parameters, a , b , and c, differ by integer powers of the base q satisfy a linear relation with coefficients that are rational functions of a , b , c , q , and the variable x.
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