On the Wallis Formula

Abstract

By virtue of complex methods and tools, the authors express the famous Wallis formula as a sum involving binomial coefficients, establish the expansions for sink x and cosk x in terms of cos(mx), find the general formulas for the derivatives of sink x and cosk x, and recover the general multiple-angle formulas for sin(kx) and cos(kx), where k 2 N and m∈Z.