https://selfgravitatingfluids.education/JETohline/index.php?action=history&feed=atom&title=Template%3AMath%2FEQ_Gamma01
Template:Math/EQ Gamma01 - Revision history
2026-04-28T23:23:01Z
Revision history for this page on the wiki
MediaWiki 1.43.1
https://selfgravitatingfluids.education/JETohline/index.php?title=Template:Math/EQ_Gamma01&diff=1592&oldid=prev
Joel2: Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> link=Appendix/SpecialFunctions#Gamma_Function </td> <td align="right" colspan="2"> <math>~ \Gamma(z) ~\Gamma(1-z) </math> </td> <td align="center"> <math>~=</math> </td> <td align="left"> <math>~ \frac{\pi}{\sin(\pi z)} </math> </td> <td align="center" rowspan="1"><math>~\biggl|</math></td> <td align="center" rowspan="3"> for example, if<br /> <math>~z \..."
2024-06-29T21:50:27Z
<p>Created page with "<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> <a href="/JETohline/index.php/File:LSUkey.png" title="File:LSUkey.png">25px|link=Appendix/SpecialFunctions#Gamma_Function</a> </td> <td align="right" colspan="2"> <math>~ \Gamma(z) ~\Gamma(1-z) </math> </td> <td align="center"> <math>~=</math> </td> <td align="left"> <math>~ \frac{\pi}{\sin(\pi z)} </math> </td> <td align="center" rowspan="1"><math>~\biggl|</math></td> <td align="center" rowspan="3"> for example, if<br /> <math>~z \..."</p>
<p><b>New page</b></p><div><table border="0" cellpadding="5" align="center"><br />
<br />
<tr><br />
<td align="right"><br />
[[Image:LSUkey.png|25px|link=Appendix/SpecialFunctions#Gamma_Function]]<br />
</td> <br />
<td align="right" colspan="2"><br />
<math>~<br />
\Gamma(z) ~\Gamma(1-z)<br />
</math><br />
</td><br />
<td align="center"><br />
<math>~=</math><br />
</td><br />
<td align="left"><br />
<math>~<br />
\frac{\pi}{\sin(\pi z)} <br />
</math><br />
</td><br />
<td align="center" rowspan="1"><math>~\biggl|</math></td><br />
<td align="center" rowspan="3"><br />
for example, if<br /><br />
<math>~z \rightarrow (m-n + \tfrac{1}{2})</math><br />
<table border="0" cellpadding="5" align="center"><br />
<tr><br />
<td align="right"><br />
<math>~\Rightarrow ~~~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})</math><br />
</td><br />
<td align="center"><br />
<math>~=</math><br />
</td><br />
<td align="left"><br />
<math>~\pi \biggl\{\sin\biggl[ \frac{\pi}{2} + \pi(m-n) \biggr] \biggr\}^{-1}</math><br />
</td><br />
</tr><br />
<br />
<tr><br />
<td align="right"><br />
&nbsp;<br />
</td><br />
<td align="center"><br />
<math>~=</math><br />
</td><br />
<td align="left"><br />
<math>~\pi (-1)^{m-n} </math><br />
</td><br />
</tr><br />
</table><br />
</td><br />
</tr><br />
<tr><br />
<td align="center" colspan=5><br />
[https://dlmf.nist.gov/5.5#ii DLMF &sect;5.5(ii)]<br />
</td><br />
<td align="center" rowspan="1"><math>~\biggl|</math></td><br />
</tr><br />
<br />
<tr><br />
<td align="right" colspan="2">Valid for: </td><br />
<td align="left" colspan="3"><br />
&nbsp; &nbsp;<math>~z \ne0, \pm 1, \pm 2, </math> &hellip;<br />
</td><br />
<td align="center" rowspan="1"><math>~\biggl|</math></td><br />
</tr><br />
</table></div>
Joel2