Gamma function note

Gamma[1]

Normalization of gamma distribution:

Integrate[x^(α-1)Exp[-x/β],{x,0,Infinity},Assumptions->(α>0&&β>0)]

?GammaDistribution

Manipulate[Plot[PDF[GammaDistribution[α,β],x],{x,0,120}],{{α,1},0,20},{{β,1},0,20}]