VisTrails Home

User:Tohline/Math/EQ Gamma01

From VisTrailsWiki

Jump to: navigation, search

~
\Gamma(z) ~\Gamma(1-z)

~=

~
\frac{\pi}{\sin(\pi z)}

~\biggl|

for example, if
~z \rightarrow  (m-n + \tfrac{1}{2})

~\Rightarrow ~~~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})

~=

~\pi \biggl\{\sin\biggl[ \frac{\pi}{2} + \pi(m-n) \biggr]  \biggr\}^{-1}

 

~=

~\pi (-1)^{m-n}

DLMF §5.5(ii)

~\biggl|
Valid for:

   ~z \ne0, \pm 1, \pm 2,

~\biggl|
Personal tools