Asymptotic expansions for a class of q-integral transforms

Using the q-Mellin transform studied in [A.Fitouhi, N. Bettaibi, K. Brahim, The Mellin transform in quantum calculus, Constructive Approximation 23 (3) ( 2006) 305 - 323], we provide an asymptotic expansion for a class of q-integral transforms having the form integral(infinity)(0) f(t)h(xt)d(q)t. In particular, we are interested with the q-Laplace, q-Fourier- cosine and q-Hankel transforms. We adopt the method of Handelsman and Lew [ R. Wong, Asymptotic Approximations of integrals, Computer Science and Scientific Computing, Academic Press, New York, 1989]. (c) 2007 Elsevier Inc. All rights reserved.