Wallis Cosine Formula

Author

Eric W. Weisstein
May 3, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/WallisCosineFormula.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/WallisCosineFormula.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Cosine

v4.2.1

Integrate[Cos[x]^n,{x,0,π/2}]

v5.0.1

Integrate[Cos[x]^n,{x,0,π/2}]

v5.1

Integrate[Cos[x]^n,{x,0,π/2}]

Sine

v4.2

Integrate[Sin[x]^n,{x,0,π/2}]

v5.0

Integrate[Sin[x]^n,{x,0,π/2}]

v5.1

Integrate[Sin[x]^n,{x,0,π/2}]

Table

Table[(((Sqrt[π]) Gamma[((1+n)/2)])/(n Gamma[(n/2)])),{n,10}]

Table[(n-1)!!/n!!If[EvenQ[n],Pi/2 ,1],{n,10}]