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Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
Published/Copyright:
April 26, 2014
Abstract.
In this paper, the expansion of a basic confluent hypergeometric function in terms of an incomplete q-gamma function is investigated and shown to be an asymptotic expansion for a basic confluent hypergeometric function and a q-analogue of the Hadamard expansion. The general expansion associated with a basic hypergeometric function is introduced. In special cases, this provides alternative derivations of the q-Hadamard expansion. Expansions and asymptotics for modified q-Bessel functions are derived as special cases from the general expansion.
Keywords: Basic hypergeometric functions; incomplete q-gamma function; modified q-Bessel functions; expansions and asymptotics
I am grateful to the referees for the valuable comments and useful suggestions, which were helpful for improving the presentation and quality of the paper.
Received: 2011-6-30
Revised: 2014-3-1
Accepted: 2014-3-10
Published Online: 2014-4-26
Published in Print: 2014-6-1
© 2014 by Walter de Gruyter Berlin/Boston
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Keywords for this article
Basic hypergeometric functions;
incomplete q-gamma function;
modified q-Bessel functions;
expansions and asymptotics
Articles in the same Issue
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- Coupled coincidence point results for (φ,ψ)-contractive mappings in partially ordered metric spaces
- q-Dunkl-classical q-Hermite type polynomials
- Spectral representation of a Banach-valued stationary random function on a locally compact abelian group
- Sharp weighted norm inequalities for the commutator of Littlewood–Paley operators
- On rearrangement theorems in Banach spaces
- Dynamical contact problems with friction for hemitropic elastic solids
- Multiple solutions for a Dirichlet quasilinear system containing a parameter
- Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1
- A priori estimates of solutions of nonlinear boundary value problems for singular in a phase variable second order differential inequalities
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- Expansions and asymptotics associated with basic hypergeometric functions and modified q-Bessel functions
