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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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Certain Summation Formulae for Basic Hypergeometric Series
Canadian Mathematical Bulletin, 1977In 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, 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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Factors of a Kind of Truncated Basic Hypergeometric Series
Bulletin of the Malaysian Mathematical Sciences SocietyThe 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)].
Li, Long, Wang, Su-Dan
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The Saalschütz chain reactions and bilateral basic hypergeometric series
Constructive Approximation, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Basic Hypergeometric Series and Applications.
The American Mathematical Monthly, 1990Ranjan Roy, Nathan J. Fine
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A Quadratic Transformation of a Basic Hypergeometric Series
SIAM Journal on Mathematical Analysis, 1980openaire +1 more source
Someq-supercongruences for truncated forms of squares of basic hypergeometric series
Journal of Difference Equations and Applications, 2021exaly