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].