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Results old and new on the hyper-Bessel equation

Published online by Cambridge University Press:  14 November 2011

R. B. Paris  and
A. D. Wood
R. B. Paris
Affiliation:
Association Euratom-CEA, Centre d'Etudes Nucléaires de Cadarache, 13108 St. Paul-lez-Durance, France
A. D. Wood
Affiliation:
National Institute for Higher Education, Glasnevin, Dublin 9, Ireland
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Synopsis

We consider a variety of integral representations, single and multiple, old and new, for solutions of the hyper-Bessel equation u(n) – zmu =0. In particular, we show how a very early multiple Laplace integral solution of Molins (1876) may be related to recent Mellin–Barnes integral representations given by the present authors by way of multiple integral solutions given by Saxton and the second author for an associated equation. Although both these multiple integral solutions may be found by elementary methods, it is not easy to find their asymptotic expansions for large z, and we show how these may conveniently be obtained from our earlier results [10].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 259 - 265
Copyright
Copyright © Royal Society of Edinburgh 1987

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