Asymptotic expansions for a class of \(q\)-integral transforms (Q2425999)

One of the famous techniques which is used in asymptotic approximation of integrals is the so-called Mellin transform technique. Recently, the \(q\)-analoque of the Mellin transform has been studied by \textit{A. Fitouhi}, \textit{N. Bettaibi} and \textit{K. Brahim} [Constructive Approximation 23, No. 3, 305--323 (2006; Zbl 1111.33006)]. In this paper, the authors continue the work presented in [\textit{Ah. Fitouhi} and \textit{N. Bettaibi} [J. Math. Anal. Appl. 328, No. 1, 518--534 (2007; Zbl 1105.33013)]. They adopt the method of Handelsman and Lew [cf. \textit{R. Wong}, Asymptotic approximations of integrals. Corrected reprint of the 1989 original. Classics in Applied Mathematics 34. Philadelphia, PA: SIAM (2001; Zbl 1078.41001)] in order to give an asymptotic expansion for a wide class of functions having the form \(F_q(x)\), even in the empty common strip case. Much attention is devoted to the so-called \(q\)-Laplace, \(q\)-Fourier-cosine and \(q\)-Hankel transforms.