Borel summation
= Borel summation
{c}
{title2=$\int_0^\infty e^{-zt}\mathcal B(t)\,dt$}
For a formal inverse-power series $\sum_{n\geq0}a_nz^{-n-1}$, divide its coefficients by $n!$ to form a Borel transform $\sum a_nt^n/n!$ and integrate it against $e^{-zt}$. Singularities on the integration ray require a specified contour prescription. Different lateral contours can produce exponentially small differences and the <Stokes phenomenon>.