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Question Number 139483 by qaz last updated on 27/Apr/21

Γ(z^− )=Γ(z)^(−)     why?

$$\Gamma\left(\overset{−} {{z}}\right)=\overline {\Gamma\left({z}\right)}\:\:\:\:{why}? \\ $$

Answered by mnjuly1970 last updated on 27/Apr/21

  hint    Γ(z)=e^(−γz) (1/z) Π_(k=1) ^∞ ((e^(z/k)   )/(1+(z/k)))   z→z^−  ......

$$\:\:{hint} \\ $$$$\:\:\Gamma\left({z}\right)={e}^{−\gamma{z}} \frac{\mathrm{1}}{{z}}\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{{e}^{\frac{{z}}{{k}}} \:\:}{\mathrm{1}+\frac{{z}}{{k}}} \\ $$$$\:{z}\rightarrow\overset{−} {{z}}\:...... \\ $$

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