evaluating the gamma function at 1/2
In the entry on the gamma function it is mentioned that . In this entry we reduce the proof of this claim to the problem of computing the area under the bell curve. First note that by definition of the gamma function,
Performing the substitution , we find that , so
where the last equality holds because is an even function. Since the area under the bell curve is , it follows that .
|Title||evaluating the gamma function at 1/2|
|Date of creation||2013-03-22 16:57:13|
|Last modified on||2013-03-22 16:57:13|
|Last modified by||CWoo (3771)|