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A Tauberian Theorem For The Riemann-Liouville Integral Of Integer Order

Published online by Cambridge University Press:  20 November 2018

C. T. Rajagopal
C. T. Rajagopal*
Affiliation:
Ramanujan Institute of Mathematics Madras, India
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 487 - 499
Copyright
Copyright © Canadian Mathematical Society 1957

References

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