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Asymptotic representation of Laplace transforms with an application to inverse factorial series

Published online by Cambridge University Press:  20 January 2009

A. Erdélyi
A. Erdélyi
Affiliation:
Mathematical Institute, The University, Edinburgh, 1.
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In a recent paper Professor A. C. Aitken directed attention to a little known type of inverse factorial series, which he calls inverse central factorial series. He showed that this type of series is a very powerful means of asymptotic representation of functions of a certain type, and concluded his note with the-remark that there is here scope for considerable investigation. As a modest contribution to this investigation, the asymptotic theory, foreshadowed in the last paragraph of Aitken's paper, will be given here: it is hoped to give the convergence theory of inverse central factorial series later.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , Issue 1 , October 1947 , pp. 20 - 24
Copyright
Copyright © Edinburgh Mathematical Society 1947

References

page 20 note 1 These Proceedings 7, 168–170 (1946).Google Scholar

page 21 note 1 Doetsch, G., Laplace Transformation (1937), p. 13.Google Scholar

page 22 note 1 Widder, D. V.The Laplace Transform (1941), Chapter V, § 1.Google Scholar