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An asymptotic expansion for the \(q\)-binomial series using singularity analysis for generating functions. (English) Zbl 1126.05019

The authors apply the method of singularity analysis, introduced by P. Flajolet and A. Odlyzko [SIAM J. Discrete Math. 3, No. 2, 216–240 (1990; Zbl 0712.05004)], to the generating function of the \(q\)-binomial series and obtain an asymptotic expression for the series. They also present an analogue of a hypergeometric function and some applications of the \(q\)-binomial series and the Gauss coefficients.

MSC:

05A30 \(q\)-calculus and related topics
05A10 Factorials, binomial coefficients, combinatorial functions
11B65 Binomial coefficients; factorials; \(q\)-identities

Citations:

Zbl 0712.05004

Software:

qseries
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Full Text: DOI

References:

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