Exponential of a Quartic
I know there is a related post regarding this, but does anyone know a
'closed' form solution for the integral
\begin{equation}I=\int_{-\infty}^{\infty} dx\,e^{ax-bx^{4}}\end{equation}
I know you can do a series expansion of the quartic term, but I'd like to
find a way that avoids that. The integral should converge as $e^{-bx^{4}}$
dominates at large $x$ and so the integrand quickly goes to zero. Any
help/ references would be greatly appreciated.
No comments:
Post a Comment