The \textit{q-j}\(_\alpha\) Bessel function
type: Item
instance of: scholarly article
title: The \textit{q-j}\(_\alpha\) Bessel function
zbMATH Open document ID: 1003.33007
author: Ahmed Fitouhi
author: M. Moncef Hamza
author: Fethi Bouzeffour
published in: Journal of Approximation Theory
publication date: 2002-08-07T00:00:00Z
review text: The authors study a \(q\)-analogue of the Bessel function \(j_{\alpha}(x)\) given by \[ j_{\alpha}(x)=2^{\alpha}\Gamma(\alpha+1)x^{-\alpha}J_{\alpha}(x), \] where \(J_{\alpha}(x)\) denotes the classical Bessel function of the first kind (of order \(\alpha\)). Several properties of these \(q\)-Bessel functions are obtained such as a number of \(q\)-integral representations and a convolution property.
reviewed by: Roelof Koekoek
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 1750344
zbMATH Keywords: \(q\)-analogue of the Bessel function
zbMATH Keywords: \(q\)-derivative
zbMATH Keywords: \(q\)-integral
MaRDI profile type: Publication
full work available at URL: jath.2001.3645
OpenAlex ID: W2076026597
cites work: Q3724706
cites work: Ted Chihara and his work on orthogonal polynomials
cites work: Q4760447
cites work: The Finite Calculus Associated with Bessel Functions
cites work: Elements of q-harmonic analysis
cites work: Q3728599
cites work: The \(q\)-cosine Fourier transform and the \(q\)-heat equation
cites work: Heat ``polynomials'' for a singular differential operator on (0,\(\infty)\)
cites work: Q4040884
cites work: Q5540735
cites work: Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
cites work: On q-Analogues of the Fourier and Hankel Transforms
cites work: The q-analogue of the Laguerre polynomials
cites work: Expansions in Terms of Heat Polynomials and Associated Functions
cites work: The Structure of the Algebra of Hankel Transforms and the Algebra of Hankel-Stieltjes Transforms
cites work: On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
cites work: Q5769133
cites work: Transformation intégrale de Weyl et théorème de Paley-Wiener associes à un opérateur différentiel singulier sur \((0,\infty)\)
cites work: Q4856171
DOI: 10.1006/JATH.2001.3645
Recommended article: Certain properties of the \(q\)-\(\ell \)-\(\varPsi \) Bessel function
Recommended article: Q3768969
Recommended article: On \(q\)-Gamma and \(q\)-Bessel functions
Recommended article: Bessel equation and Bessel function on $\mathbb{T}_{(q,h)}$
Recommended article: The Bessel operator function
Recommended article: Generalized \(q\)-Bessel function and its properties
Recommended article: About Jackson \(q\)-Bessel functions
Recommended article: The Bessel zeta function
Recommended article: Q3167230
Recommended article: Q4398582
description: scientific article; zbMATH DE number 1750344