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Some recurrence relations and series for the generalised laplace transform

Published online by Cambridge University Press:  18 May 2009

B. R. Bhonsle
B. R. Bhonsle
Affiliation:
Government Engineering College, Jabalpur, M.P., India
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The Laplace transform

has been generalised by Varma [4] by the relation

which reduces to (1.1) when k = -m + ½ by virtue of the identity

We shall define πk, m, λ (p) by the relation

The object of this paper is to obtain some recurrence formulae and series for πk, m, λ (p) and to use them to obtain recurrence formulae and series for MacRobert's E-function.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 3 , January 1960 , pp. 119 - 121
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

References

1.Harishanker, , Proc. Benares Math. Soc., 4 (1942), 51–57.Google Scholar
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3.Saksena, K. M., Proc. Nat. Acad. Sci. India, 21 (1953), 202–208.Google Scholar
4.Varma, R. S., Proc. Nat. Acad. Sci. India, 20 (1951), 209.Google Scholar
5.Whittaker, E. T. and Watson, G. N., Modern analysis, 4th edn (Cambridge, 1940).Google Scholar