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An Extension of Abel's Theorem on the Continuity of a Power Series

Published online by Cambridge University Press:  20 January 2009

Gibson
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When the series

is convergent, then Abel's Theorem shows that

Series of the form

are of frequent occurrence in the Analytical Theory of Heat and in other branches of Mathematical Physics, and the conditions to which f(t) is subject usually require that as t tends to zero the function f(t) should tend to the value s.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , February 1900 , pp. 67 - 70
Copyright
Copyright © Edinburgh Mathematical Society 1900