On the arithmetic of Padé approximants to the exponential function

John Cullinan, Nick Scheel

The $(u,v)$-Padé approximation to a function $f$ is the (unique, up to scaling) rational approximation $f(x)=P(x)/Q(x)+O(x^{u+v+1})$, where $P$ has degree $u$ and $Q$ has degre…