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On Frullani Integrals

Published online by Cambridge University Press:  24 October 2008

K. S. K. Iyengar
K. S. K. Iyengar
Affiliation:
Central CollegeBangaloreIndia
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Extract

The object of this note is to obtain necessary and sufficient conditions for the existence of

on the assumption that ø is integrable in any finite positive interval not including zero (0 < α ≤ x ≤ β < ∞). On reference to the literature on the topic, I find no exhaustive analysis of this problem anywhere.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 37 , Issue 1 , January 1941 , pp. 9 - 13
Copyright
Copyright © Cambridge Philosophical Society 1941

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References

* See, for example, Hardy, , Messenger of Math. 34 (1905), 11–18;Google ScholarBromwich, , Infinite series, 2nd ed. (1926), 479;Google ScholarPoussin, de la Vallée, Cours d'analyse, 6th ed. (1926), ii, 34.Google Scholar