微分と積分の関係
\[
f\left(x\right)=\int_{f^{\bullet}\left(a\right)}^{x}f'\left(x\right)dx-a
\]
NEW!ガンマ関数を2つ含む定積分でカタラン定数が出てきます
\[
\int_{0}^{\frac{1}{2}}\Gamma\left(1-x\right)\Gamma\left(1+x\right)dx=?
\]
中央2項係数の値
\[
C\left(2n,n\right)=4^{n}\left(-1\right)^{n}C\left(-\frac{1}{2},n\right)
\]
階乗と階乗の逆数の母関数
\[
\frac{x^{a}}{a!}=e^{x}\left(\frac{\Gamma\left(a+1,x\right)}{\Gamma\left(a+1\right)}-\frac{\Gamma\left(a,x\right)}{\Gamma\left(a\right)}\right)
\]