Difference between revisions of "User:Tohline/Math/EQ Gamma01"
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| (11 intermediate revisions by the same user not shown) | |||
| Line 15: | Line 15: | ||
<td align="left"> | <td align="left"> | ||
<math>~ | <math>~ | ||
\frac{\pi}{\sin(\pi z)} | \frac{\pi}{\sin(\pi z)} | ||
</math> | </math> | ||
</td> | |||
<td align="center" rowspan="1"><math>~\biggl|</math></td> | |||
<td align="center" rowspan="3"> | |||
for example, if<br /> | |||
<math>~z \rightarrow (m-n + \tfrac{1}{2})</math> | |||
<table border="0" cellpadding="5" align="center"> | |||
<tr> | |||
<td align="right"> | |||
<math>~\Rightarrow ~~~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~\pi \biggl\{\sin\biggl[ \frac{\pi}{2} + \pi(m-n) \biggr] \biggr\}^{-1}</math> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td align="right"> | |||
| |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~\pi (-1)^{m-n} </math> | |||
</td> | |||
</tr> | |||
</table> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 23: | Line 53: | ||
[https://dlmf.nist.gov/5.5#ii DLMF §5.5(ii)] | [https://dlmf.nist.gov/5.5#ii DLMF §5.5(ii)] | ||
</td> | </td> | ||
<td align="center" rowspan="1"><math>~\biggl|</math></td> | |||
</tr> | </tr> | ||
| Line 30: | Line 61: | ||
<math>~z \ne0, \pm 1, \pm 2, </math> … | <math>~z \ne0, \pm 1, \pm 2, </math> … | ||
</td> | </td> | ||
<td align="center" rowspan="1"><math>~\biggl|</math></td> | |||
</tr> | </tr> | ||
</table> | </table> | ||
Latest revision as of 00:08, 15 June 2018
|
|
<math>~ \Gamma(z) ~\Gamma(1-z) </math> |
<math>~=</math> |
<math>~ \frac{\pi}{\sin(\pi z)} </math> |
<math>~\biggl|</math> |
for example, if
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| <math>~\biggl|</math> | ||||||||||||
| Valid for: |
<math>~z \ne0, \pm 1, \pm 2, </math> … |
<math>~\biggl|</math> | ||||||||||
