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Examples of Equation (2.3)

\begin{align*}
&If\text{ }s=2.7,&\Gamma \left( 3.7 \right)&=\Gamma (0.7)\cdot \left( 2.7 \right)\cdot \left( 1.7 \right)\cdot \left( 0.7 \right)=4.1707 \\
&If\text{ }s=-3.7,&\Gamma \left( -2.7 \right)&=\Gamma (0.3)\cdot \frac{1}{-2.7}\cdot \frac{1}{-1.7}\cdot \frac{1}{-0.7}=-0.9311 \\
&If\text{ } s=4, &\Gamma \left( 5 \right)&=\Gamma \left( 1 \right)\cdot \left( 4 \right)\cdot \left( 3 \right)\cdot \left( 2 \right)\cdot \left(1 \right)=24
\end{align*}

$h_{s}^{c}$ is closely related to $\Gamma \left( s \right)$ when $c\to -\infty $, where $0<s\le 1$.

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