On Laplace Transforms Near the Origin
نویسندگان
چکیده
Let /(f) be locally integrable on [0, °°) and let L{f}(s) denote the Laplace transform of /(f). In this note, we prove that if/(f) ~ f Sh=q an(log f)~ as f -> °°, where 0 < Re ß < 1, then /.{/}($) ~ s^1 2^=0 cn('°8 '/*)"" as s ->• 0 in larg si « 7r/2 A, the cn being constants.
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