V.—On the Orthogonal Polynomials in Frequencies of Type B

Abstract

The orthogonal properties of the Hermite polynomials, their relation to the normal frequency function, and the part they play in expressing the more general frequency function of Type A, are matters of common knowledge in mathematical statistics. Less well known are the very similar properties of a class of polynomials related in the same kind of way to Poisson's frequency function of rare events and to the function of Type B which generalizes Poisson's function. These polynomials have been interestingly studied during the last few years by Ch. Jordan and by H. Pollaczek-Geiringer. (References are given at the end of this paper.) In preparation for our main object we shall gather together the principal results concerning these polynomials, together with a few others not mentioned in the extant literature.