古德温 - 斯塔顿积分(英语:Goodwin-Staton Integral)定义如下
G ( z ) = ∫ 0 ∞ e − t 2 t + z d t {\displaystyle G(z)=\int _{0}^{\infty }\!{\frac {{\rm {e}}^{-{t}^{2}}}{t+z}}{dt}}
它是下列三阶非线性常微分方程的一个解: 4 w ( z ) + 8 z d d z w ( z ) + ( 2 + 2 z 2 ) d 2 d z 2 w ( z ) + z d 3 d z 3 w ( z ) = 0 {\displaystyle 4\,w\left(z\right)+8\,z{\frac {d}{dz}}w\left(z\right)+\left(2+2\,{z}^{2}\right){\frac {d^{2}}{d{z}^{2}}}w\left(z\right)+z{\frac {d^{3}}{d{z}^{3}}}w\left(z\right)=0}
G ( − z ) = G ( z ) {\displaystyle G(-z)=G(z)}