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

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for example, if<br />
for example, if<br />
<math>~z \rightarrow  (m-n + \tfrac{1}{2})</math>
<math>~z \rightarrow  (m-n + \tfrac{1}{2})</math>
  </td>
  <td align="center" rowspan="3">&nbsp; &nbsp; &nbsp; <math>~\Rightarrow</math>&nbsp; &nbsp; </td>
  <td align="center" rowspan="3">
<table border="0" cellpadding="5" align="center">
<table border="0" cellpadding="5" align="center">
<tr>
<tr>
   <td align="right">
   <td align="right">
<math>~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})</math>
<math>~\Rightarrow ~~~\Gamma(m-n+\tfrac{1}{2})~\Gamma(n-m+\tfrac{1}{2})</math>
   </td>
   </td>
   <td align="center">
   <td align="center">

Latest revision as of 00:08, 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 ~~~\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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