Prove a seguinte propriedade da função gamma para todo n nos naturais:

[tex]\Gamma\left(\dfrac{1}{2}+n\right)=\dfrac{1\cdot3\cdot5\dots(2n-1)}{2^n}\sqrt{ \pi}\\[/tex]

Use indução finita.

Obs: Cálculos auxiliares para o problema:

[tex] \begin{cases}\Gamma\left(\dfrac{1}{2}\right)=\sqrt{\pi}\\\\\Gamma\left(\dfrac{3}{4}\right)=\dfrac{\sqrt{\pi}}{2}\\ \\ \Gamma\left( \dfrac{7}{2} \right)=\dfrac{15\sqrt{\pi}}{4} \\ \\\Gamma\left(x+1\right)=x\Gamma(x) \end{cases}[/tex]
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