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XV.—Theorems on the Convergence and Asymptotic Validity of Abel's Series*

Published online by Cambridge University Press:  14 February 2012

A. J. Macintyre  and
Sheila Scott Macintyre
A. J. Macintyre
Affiliation:
University of Aberdeen
Sheila Scott Macintyre
Affiliation:
University of Aberdeen
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Synopsis

In this paper we discuss the Abel series for a function F(z) which is regular in an angle | arg z | ≤ α and at the origin. We investigate conditions under which the series converges and conditions under which its sum is asymptotically equivalent to the function F(z) in the half-plane R(z) > 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 3 , 1952 , pp. 222 - 231
Copyright
Copyright © Royal Society of Edinburgh 1952

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References

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