Let the random variable ξ be distributed with distribution function G(ξ) of the continuous, discontinuous or mixed type, and the random variables xξ be distributed with the distribution functions Vξ(x) with the corresponding characteristic functions , η being a real variable, and i the imaginary unit, and with the generating functions defined by ψξ(− i log z). If the range of x is restricted to the right semi-plane the lower limit of the integral in the definition of ψξ(η) can be replaced by zero.