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Some Integrals Involving E-Functions

Published online by Cambridge University Press:  18 May 2009

R. K. Saxena
R. K. Saxena
Affiliation:
Maharana Bhupal College, Udaipur
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In this paper we evaluate some integrals involving U-functions by the methods of the Operational Calculus. The results obtained are quite general and many of them include, as particular cases, some known results.

A function ψ (p) is operationally related with another function f(t), if they satisfy the integral equation

2. Theorem. If

and

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

provided that the integral is convergent. HereR(α) > 0, R(p) > 0, n = 2,3,4, …, andmeans that in the expression following it, i is to bee replaced by – i and the two expressions are to be added.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 4 , September 1960 , pp. 178 - 185
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

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