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Some theorems on fractional integrals

Published online by Cambridge University Press:  24 October 2008

T. M. Flett
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Extract

1. Let φ(z) be regular in │z│ < 1, let

and for any real α let

where (in)−α = n−α exp(— ½απi). The function φα is an adaptation to power series of the Weyl fractional integral of order a of α function of a real variable.† It exists and is regular in │z│ < 1 for all α. Let also

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 31 - 50
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

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