Indefinite Integration of the Gamma Integral
and Related Statistical Applications

Proof of Equation (3.4)

$$\begin{equation*} h_{s}^{p-q}=\sum\limits_{i=0}^{\infty }{\frac{{{\left( -q \right)}^{i}}}{i!}\frac{{{\partial }^{\left( i \right)}}h_{s}^{p}}{\partial {{p}^{i}}}}. \end{equation*}$$ Proof:
Replacing $q$ with $-q$ in the summation formula (3.3), we can derive the subtraction formula.

$\square$

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