Abstract
In this paper, we study in quantum calculus the correspondence between poles of the
q-Mellin transform (see [A. Fitouhi, N. Bettaibi, K. Brahim, The Mellin transform in Quantum Calculus, Constr. Approx. 23 (3) (2006) 305–323]) and the asymptotic behaviour of the original function at 0 and ∞. As applications, we give a new technique (in
q-analysis) to derive the asymptotic expansion of some functions defined by
q-integrals or by
q-harmonic sums. Finally, a
q-analogue of the Mellin–Perron formula is given.