Scaled asymptotics for some \(q\)-functions (Q651056)
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scientific article; zbMATH DE number 5987738
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Scaled asymptotics for some \(q\)-functions |
scientific article; zbMATH DE number 5987738 |
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Scaled asymptotics for some \(q\)-functions (English)
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8 December 2011
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In 2006-2007, the author and M. E. Ismail applied a new method to Plancherel-Rotach type asymptotics for certain sets of orthogonal polynomials. Later, in 2008, the author extended the method to study certain Plancherel-Rotach type asymptotics for some \(q\)-series. In this paper, employing these asymptotic formulae, he studies the scaled asymptotics of some generalized \(q\)-series as \(q\to 1\) by using admissible sequences.
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\(q\)-series
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\(q\)-orthogonal polynomials
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\(q\)-Airy function
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Jackson's \(q\)-Bessel function
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\(q^{-1}\)-Hermite polynomials
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\(q\)-Laguerre polynomials
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Plancherel-Rotach asymptotics
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theta functions
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confluent basic hypergeometric series
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scaled asymptotics
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