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

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</math>
</math>
   </td>
   </td>
   <td align="center" rowspan="1">&nbsp; &nbsp; &nbsp; <math>~\biggl|</math></td>
   <td align="center" rowspan="1"><math>~\biggl|</math></td>
   <td align="center" rowspan="3">
   <td align="center" rowspan="3">
for example, if<br />
for example, if<br />
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[https://dlmf.nist.gov/5.5#ii DLMF &sect;5.5(ii)]
[https://dlmf.nist.gov/5.5#ii DLMF &sect;5.5(ii)]
   </td>
   </td>
   <td align="center" rowspan="1">&nbsp; &nbsp; &nbsp; <math>~\biggl|</math></td>
   <td align="center" rowspan="1"><math>~\biggl|</math></td>
</tr>
</tr>


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&nbsp; &nbsp;<math>~z \ne0, \pm 1, \pm 2, </math> &hellip;
&nbsp; &nbsp;<math>~z \ne0, \pm 1, \pm 2, </math> &hellip;
   </td>
   </td>
   <td align="center" rowspan="1">&nbsp; &nbsp; &nbsp; <math>~\biggl|</math></td>
   <td align="center" rowspan="1"><math>~\biggl|</math></td>
</tr>
</tr>
</table>
</table>

Revision as of 00:01, 15 June 2018

LSU Key.png

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

<math>~=</math>

<math>~ \frac{\pi}{\sin(\pi z)} \, . </math>

<math>~\biggl|</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>

DLMF §5.5(ii)

<math>~\biggl|</math>
Valid for:

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

<math>~\biggl|</math>
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