On the numerical evaluation of two infinite products

Abstract

A numerical evaluation of two infinite products of the type Π n = 0 ∞ ( 1 − a q n ) \Pi _{n = 0}^\infty (1 - a{q^n}) , which are important in some mathematical fields, is considered. The numerical evaluation is based on a recursive formula of the type x n + 1 = x n f ( y n / x n ) {x_{n + 1}} = {x_n}f({y_n}/{x_n}) , y n + 1 = x n + 1 g ( y n / x n ) {y_{n + 1}} = {x_{n + 1}}g({y_n}/{x_n}) , and it is compared with a series expansion that was previously used for the computation. Two tables of the infinite products are provided with twenty significant figures which check and extend existing data.