Wallis product

English

Etymology

Published in 1656 by John Wallis.

Proper noun

1. Template:Lb An infinite product that approximates half of pi: $\begin{array}{cc}\frac{\pi }{2}& =\prod _{n=1}^{\mathrm{\infty }}\frac{4n^2}{4n^2-1}=\prod _{n=1}^{\mathrm{\infty }}(\frac{2n}{2n-1}\cdot \frac{2n}{2n+1})\\ & =(\frac{2}{1}\cdot \frac{2}{3})\cdot (\frac{4}{3}\cdot \frac{4}{5})\cdot (\frac{6}{5}\cdot \frac{6}{7})\cdot (\frac{8}{7}\cdot \frac{8}{9})\cdot \cdots \\ \end{array}$.