Zeros of entire functions and a problem of Ramanujan
TLDR
In this paper, the authors derive representations for certain entire q-functions and apply their technique to the Ramanujan entire function (or q -Airy function) and q -Bessel functions.About:
This article is published in Advances in Mathematics.The article was published on 2007-02-15 and is currently open access. It has received 39 citations till now. The article focuses on the topics: Ramanujan tau function & Ramanujan theta function.read more
Citations
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Book ChapterDOI
q -Difference Equations
TL;DR: In this article, Mansour et al. presented proofs of the existence and uniqueness of the solutions of first order systems of q-difference equations in a neighborhood of a point a, \(a \geq 0\).
Journal ArticleDOI
On the zeros of the second and third Jackson q-Bessel functions and their associated q-Hankel transforms
TL;DR: In this paper, the authors investigated the zeros of q-Bessel functions of the second and third types as well as those of the associated finite q-Hankel transforms.
Journal ArticleDOI
Chaotic and periodic asymptotics for q-orthogonal polynomials
TL;DR: In this article, the authors derive Plancherel-Rotach asymptotic expansions for the q �1 -Hermite, q-Laguerre, and Stieltjes-Wigert polynomials using a discrete analogue of Laplace's method.
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$q$-Bessel functions and Rogers-Ramanujan type identities
TL;DR: In this paper, a generalization of the Ramanujan function and a generalized version of the Rogers-Ramanujan identity were presented for generating functions for Stieltjes-Wigert polynomials with argument depending on the degree.
References
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Book
A treatise on the theory of Bessel functions
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Book
A Course of Modern Analysis
TL;DR: The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.
Posted Content
Orthogonal Polynomials
TL;DR: In this paper, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed and orthogonality on the unit circle is not discussed.
Book
Basic Hypergeometric Series
George Gasper,Mizan Rahman +1 more
TL;DR: In this article, the Askey-Wilson q-beta integral and some associated formulas were used to generate bilinear generating functions for basic orthogonal polynomials.