Asymptotic expansions for a class of q-integral transforms

Abstract

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 ∫ 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].