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On Asymptotic Expansion of Generalized Mellin-Whittaker Transform

R. V. Kene and A. S. Gudadhe

In this article, we investigate the asymptotic behaviour at infinity of the generalized Mellin-Whittaker transform of the form.

MW (k,m) f ] (s, y) = ∫ 0 ∞ ∫ 0 ∞ x (s −1)e (−yt /(2))) yt W (k,m) (yt) f (x,t) dxd

Involving the Whittaker function Wk,m (z) inthekernel. It is proved that [MW (k,m)↑ρ f ] (s, y) ↓ has power or power logarithmic asymptotic expansion as s → ∞ and y → ∞ provided that f (x,t) has power asymptotic behaviour at infinity.