ON THE GENERAL ASYMPTOTIC EXPANSIONS OF H_V ⁽¹⁾-TRANSFORM AND RELATED BESSEL TRANSFORMS

Theorems are established to give the asymptotic expansions of Hv(1) - transforms and related Bessel transforms of functions which have general asymptotic expansions near the origin. The results are thus the extensions to those of the existing literature (e.g. Wong 1976, Soni 1982 and Soni&Soni 1985) which dealt with the cases that the functions have power expansions near the origin. Our approach uses a lemma proved in an earlier paper (Dai 1992) on the general asymptotic expansions of Kv - transforms and adopts a novel method to overcome divergent integrals.