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Some infinite integrals involving E-functions

Published online by Cambridge University Press:  18 May 2009

R. K. Saxena
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A function φ(p) is operationally related to h(t) when they satisfy the integral equation

provided that the integral is convergent and R(p)> 0.

As usual, we shall denote (1) by the symbolic expression

φ(p) ≑ h(t).

The object of this paper is to evaluate some infinite integrals involving E-functions by the methods of the operational calculus. Most of the results obtained are believed to be new.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 4 , July 1962 , pp. 183 - 187
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Erdélyi, A., Higher transcendental functions, Vol. I (New York, 1953).Google Scholar
2.Erdélyi, A., Tables of integral transforms, Vol. I (New York, 1954).Google Scholar
3.Erdélyi, A., Tables of integral transforms, Vol. II (New York, 1954).Google Scholar
4.Goldstein, S., Operational representation of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder functions, Proc. London Math. Soc. (2) 34 (1932), 103–125.CrossRefGoogle Scholar
5.Rathie, C. B., A few theorems on generalised Laplace transform, Proc. Nat. Acad. Sci., India 21 (1953), 65–74.Google Scholar