Numerical integration provides a substitute for the infinite series wherever the exact values of the probability function of z are needed. Some extensions of the main theorem are given in section 5 ...

Albert Madansky, Bounds on the Expectation of a Convex Function of a Multivariate Random Variable, The Annals of Mathematical Statistics, Vol. 30, No. 3 (Sep., 1959), pp. 743-746 ...