Published online by Cambridge University Press: 18 May 2009
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.