Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-29T10:53:18.628Z Has data issue: false hasContentIssue false
  • English
  • Français

The Laplace transform of exp(et)

Published online by Cambridge University Press:  17 February 2009

Michael A. B. Deakin
Michael A. B. Deakin
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In an earlier paper [4], the author showed how Laplace transforms might be assigned to a class of superexponential functions for which the usual defining integral diverges. The present paper considers the case of the function exp(et), which arises in combinatorial contexts and whose Laplace transform may be assigned by means of an extension of techniques described in the previous paper.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 3 , January 1996 , pp. 279 - 287
Copyright
Copyright © Australian Mathematical Society 1996

References

[1] Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical functions (Dover, New York, 1970).Google Scholar
[2] Berg, L., Introduction to the operational calculus (North Holland, Amsterdam, 1967).Google Scholar
[3] Comtet, L., Advanced combinatorics (Reidel, Dordrecht, 1974).CrossRefGoogle Scholar
[4] Deakin, M. A. B., “Laplace transforms for superexponential functions”, J. Austral. Math. Soc. Ser B., (to appear).Google Scholar
[5] Erdélyi, A. (ed.), Higher transcendental functions Vol. 2 (McGraw Hill, New York, 1953).Google Scholar
[6] Erdélyi, A. (ed.), Tables of integral transforms, Vol. 1 (McGraw Hill, New York, 1954).Google Scholar
[7] Flajolet, P., “Combinatorial aspects of continued fractions”, Discr. Math. 32 (1980) 125–161.CrossRefGoogle Scholar
[8] Flajolet, P. and Schott, R., “Non-overlapping partitions, continued fractions, Bessel functions and a divergent series”, Europ. J. Combinatorics 11 (1990) 421–432.CrossRefGoogle Scholar
[9] Vignaux, J. C., “Sugli integrali di Laplace asintotici”, Atti Accad. naz. Lincei, Rend. CI. Sci. fiz. mat. (6 ser.) 29 (1939) 396–402.Google Scholar
[10] Whittaker, E. T. and Watson, G. N., A course of modern analysis, 4th Edn. (Cambridge University Press, 1927).Google Scholar