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A Tauberian Theorem For The Riemann-Liouville Integral Of Integer Order
Published online by Cambridge University Press: 20 November 2018
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1. Notation. Let s(x) be a function integrable in every finite interval of x ≥ 0. Then the Riemann-Liouville integral of s(x), of order a > 0, is defined for x ≥ 0 by
(1).
The object of this note is to prove a Tauberian theorem for sα(x) in the case in which α is a positive integer p, employing certain difference formulae due to Karamata (4, Lemma 2) and Bosanquet (1, Theorem 1) used already for a broadly similar purpose in an earlier paper (12) where a is any positive number.
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- Copyright © Canadian Mathematical Society 1957
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