Abstract
Theorems are established to obtain the general asymptotic expansions of the Kv-transforms. It is shown that, under certain circumstances, the asymptotic expansion of Kv-transforms. F(s) as s → 0+ or s → ∞ is obtained by integrating term by term the asymptotic expansion of the function at t → ∞ or t → 0+. In the case that the function has a power expansion, the treatment of this problem can be found in the existing literature (e.g. [4],[5]). In this paper we assume that the function has a general expansion form. Three examples, including the case that the function has an exponentially small behaviour at the origin, are discussed.
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†Current address: Department of Applied Mathematics, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
†Current address: Department of Applied Mathematics, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Notes
†Current address: Department of Applied Mathematics, The University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2