Applications of the Mellin transform in quantum calculus
type: Item
instance of: scholarly article
title: Applications of the Mellin transform in quantum calculus
zbMATH Open document ID: 1105.33013
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-12T00:00:00Z
review text: In this paper the authors study in quantum calculus the correspondence between poles of the \(q\)-Mellin transform and the asymptotic behaviour of the original function at \(0\) and \(\infty\). They prove that each individual term in such asymptotic expansion of a function \(f\) taking the form \(x^{b}(\operatorname{Log} x)^{k}\), \(k \in \mathbb{N}\), is linked to a pole of its \(q\)-Mellin transform at \(s=-b\) with multiplicity \(k+1\). As applications they give a new technique to derive the asymptotic expansion of some functions defined by \(q\)-integrals or by \(q\)-harmonic sums. They also obtain a \(q\)-analogue of the generalized Euler-Maclaurin formula as well as a \(q\)-analogue of the Mellin-Perron formula.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 33D05
Mathematics Subject Classification ID: 33D60
Mathematics Subject Classification ID: 44A20
zbMATH DE Number: 5124085
zbMATH Keywords: \(q\)-analysis
zbMATH Keywords: \(q\)-Mellin transform
zbMATH Keywords: asymptotic expansions
author: Ahmed Fitouhi
author: Néji Bettaibi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.05.051
OpenAlex ID: W2060006821
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DOI: 10.1016/J.JMAA.2006.05.051
description: scientific article; zbMATH DE number 5124085