November 2019 1 393 Report
A função gama é definida, para cada x > 0, por

\mathsf{\displaystyle\Gamma(x)=\int_{0}^{\infty}e^{-u}\,u^{x-1}\,du}

Prove que, para todo x > 0, \mathsf{\Gamma(x+1)=x\,\Gamma(x)}

Conclua que a função gama interpola os fatoriais, isto é, que todo fatorial pertence à imagem de \mathsf{\Gamma}
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