= Quadratic complex endpoint descent path
{title2=$z(s)^2=b^2+s$}
For $e^{-\lambda z^2}$, the <saddle point> descent is the real axis and ascent is the imaginary axis. A descent path from a nonzero endpoint $b$ has $z(s)^2=b^2+s$, $s\geq0$, with the continuous square-root branch from $b$. It ends at positive or negative real infinity according to the sign of $\operatorname{Re}b$. The oriented outward <endpoint contribution in steepest descent> is $e^{-\lambda b^2}/(2\lambda b)$.
Back to article page
