Question

how find gamma of -15/2

Answer 1

@tHe_FiZiCx99

Answer 2

There are a handful of ways you can do this, depending on what you wanna do. You can remember this value (or derive it from the integral definition with a cute trick using the Gaussian)
\[\Gamma(\tfrac{1}{2}) = \sqrt{\pi}\]
and then remember this (or derive it from the integral definition using integration by parts)
\[\Gamma(n+1)=n\Gamma(n)\]

That's really just the Gamma version of \(n!=n*(n-1)!\) but keep in mind that the Gamma version works for non integers!

Answer 3

So now you can use this recursive definition to get \(\Gamma( \tfrac{-15}{2})\)

Here's the first step getting you closer to \(\Gamma(\tfrac{1}{2})\) so that you can exactly evaluate it:
\[ \Gamma( \tfrac{-13}{2}) = \tfrac{-15}{2}\Gamma( \tfrac{-15}{2}) \]
See if you can do this quickly rather than multiplying each and every piece.