The rational function P/Q with deg P <= m, deg Q <= n and Q(0) = 1 whose Maclaurin series agrees with e's through order m + n. Frequently a much better approximation than the Taylor polynomial of the same total degree, because a rational function can model a nearby pole that no polynomial can.
Follows _Taylor's convention that v is the expansion variable rather than a binder -- free in the result, but excluded from children so substitute cannot rewrite it. Like _FourierSeries the coefficients are numeric, so m and n must fold to non-negative integers with m + n <= MaxTaylorOrder and every Maclaurin coefficient must reduce; anything else leaves the node symbolic, including the case where the linear system is singular and no [m/n] approximant exists.
