Difference between revisions of "User:Tohline/Math/EQ Gamma01"

Revision as of 21:35, 14 June 2018

<math>~ \Gamma(z) ~\Gamma(1-z) </math>

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

<math>~\Rightarrow</math>

<math>~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})</math>	<math>~=</math>	<math>~\pi \biggl\{\sin\biggl[ \frac{\pi}{2} + \pi(m-n) \biggr] \biggr\}^{-1}</math>
	<math>~=</math>	<math>~\pi (-1)^{m-n} \, .</math>

Valid for:

<math>~z \ne0, \pm 1, \pm 2, </math> …

@@ Line 35: / Line 35: @@
    </td>
    <td align="left">
-<math>~\pi \biggl\{\sin[\pi(m-n+\tfrac{1}{2})]  \biggr\}^{-1}</math>
+<math>~\pi \biggl\{\sin\biggl[ \frac{\pi}{2} + \pi(m-n) \biggr]  \biggr\}^{-1}</math>
    </td>
 </tr>