Wallis' Integrals

Wallis' integrals are a family of integrals in mathematical analysis, defined as W_n equal to the integral from 0 to pi over 2 of sin to the power n of x dx, or equivalently of cos to the power n of x dx, for a non-negative integer n. They were introduced by the mathematician John Wallis, and the resulting sequence decreases with positive terms that converge to zero. Wallis' integrals connect to several other results in analysis, including Stirling's formula, the Gaussian integral, and the Wallis product, which expresses pi over 2 as an infinite product. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/