Question: In Example 12.15 we introduced Euler's gamma function: [Gamma(t)=int_{(0, infty)} x^{t-1} e^{-x} lambda^{1}(d x)] Show that (Gammaleft(frac{1}{2}ight)=sqrt{pi}). Data from example 12.15 Example 12.15 (Euler's gamma
In Example 12.15 we introduced Euler's gamma function:
\[\Gamma(t)=\int_{(0, \infty)} x^{t-1} e^{-x} \lambda^{1}(d x)\]
Show that \(\Gamma\left(\frac{1}{2}ight)=\sqrt{\pi}\).
Data from example 12.15
Example 12.15 (Euler's gamma function) The parameter-dependent integral ) := (0.00)*x^- e- x x (dx), (12.13) T(t):= t>0
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