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Wallis Cosine Formula

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For a positive integer n, the Wallis cosine formula evaluates the common sine and cosine forms of the Wallis integral as

int_0^(pi/2)cos^nxdx=int_0^(pi/2)sin^nxdx
(1)
=(sqrt(pi)Gamma(1/2(n+1)))/(nGamma(1/2n))
(2)
=((n-1)!!)/(n!!){1/2pi for even n; 1 for odd n.
(3)

where Gamma(n) is a gamma function and n!! is a double factorial.

See also

Wallis Formula, Wallis Integral

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Cite this as:

Weisstein, Eric W. "Wallis Cosine Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WallisCosineFormula.html

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