I have two questions related Gamma functions(adsbygoogle = window.adsbygoogle || []).push({});

1. Finding ##\Gamma## analytically. Is that possible only for integers and halfintegers? Or is it possible mayble for some other numbers? For example is it possible to find analytically ##\Gamma(\frac{3}{4})##?

2. Integral ##\Gamma(x)=\int^{\infty}_0 \xi^{x-1}e^{-\xi}d \xi ## converge only for ##x>0## in real analysis. How can we then write ##\Gamma(\frac{1}{2})=\Gamma(-\frac{1}{2}+1)## when relation ##\Gamma(x+1)=x\Gamma(x)## is derived from partial integration?

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# A Gamma function

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