Editing Half-integer (section)

===Sphere volume===
Although the [[factorial]] function is defined only for integer arguments, it can be extended to fractional arguments using the [[gamma function]]. The gamma function for half-integers is an important part of the formula for the [[volume of an n-ball|volume of an {{mvar|n}}-dimensional ball]] of radius <math>R</math>,<ref>{{cite web |title=Equation&nbsp;5.19.4 |website=NIST Digital Library of Mathematical Functions |url=http://dlmf.nist.gov/ |publisher=U.S. [[National Institute of Standards and Technology]] |id=Release&nbsp;1.0.6 |date=2013-05-06}}</ref>
<math display=block>V_n(R) = \frac{\pi^{n/2}}{\Gamma(\frac{n}{2} + 1)}R^n~.</math>
The values of the gamma function on half-integers are integer multiples of the square root of [[pi]]:
<math display=block>\Gamma\left(\tfrac{1}{2} + n\right) ~=~ \frac{\,(2n-1)!!\,}{2^n}\, \sqrt{\pi\,} ~=~ \frac{(2n)!}{\,4^n \, n!\,} \sqrt{\pi\,} ~</math>
where <math>n!!</math> denotes the [[double factorial]].