On Frullani integrals

Iyengar, K. S. K. (1941) On Frullani integrals Mathematical Proceedings of the Cambridge Philosophical Society, 37 (1). pp. 9-13. ISSN 0305-0041

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Related URL: http://dx.doi.org/10.1017/S0305004100021484


The object of this note is to obtain necessary and sufficient conditions for the existence of I(a,b) = ∫0Φ(at)-Φ(bt)dt/t (0<a<b), 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.

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