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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

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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
Copyright
Copyright © Edinburgh Mathematical Society 1900