Gamma function: Difference between revisions

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General: \Gamma(1/2-n) formula: the last equality is obvious wrong because \Gamma(-1/2)= -2\sqrt(\pi). Deleted from right = \frac{\sqrt{\pi}}{{-\frac12 \choose n} n!}
Undid revision 919739034 by Mathstat (talk) this appears to be right; in particular, it gives the same value for the n=1 case mentioned in the previous summary
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:<math>\begin{align}
\Gamma\left(\tfrac12+n\right) &= {(2n)! \over 4^n n!} \sqrt{\pi} = \frac{(2n-1)!!}{2^n} \sqrt{\pi} = \binom{n-\frac12 \choose frac{1}{2}}{n} n! \sqrt{\pi} \\[8pt]
\Gamma\left(\tfrac12-n\right) &= {(-4)^n n! \over (2n)!} \sqrt{\pi} = \frac{(-2)^n}{(2n-1)!!} \sqrt{\pi}, = \frac{\sqrt{\pi}}{\binom{-1/2}{n} n!}
\end{align}</math>