不完全ガンマ関数
∂ m Γ ( a , x ) ∂ a m = ln m  x Γ ( a , x ) + m x ∑ n = 0 m − 1 P n m − 1 ln m − n − 1  x T ( 3 + n , a , x ) {\displaystyle {\frac {\partial ^{m}\Gamma (a,x)}{\partial a^{m}}}=\ln ^{m}x\Gamma (a,x)+mx\,\sum _{n=0}^{m-1}P_{n}^{m-1}\ln ^{m-n-1}x\,T(3+n,a,x)} と P j n = ( n j ) j ! = n ! ( n − j ) ! . {\displaystyle P_{j}^{n}=\left({\begin{array}{l}n\\j\end{array}}\right)j!={\frac {n!}{(n-j)!}}.}