Numerical Method for the Exact Expansion of Generating Functions

Abstract

A new method is developed for the evaluation of coefficients in multinomial generating functions. This method requires solely numerical techniques to derive the coefficients in the expansion of the generating function, and thus avoids the organizational problems that occur when algebraic methods are used to expand these functions. With the use of a digital computer this method enables the number of coefficients to be extended considerably. As an example of its application some of the coefficients in a four‐variable generating function are calculated.