  Given a function $f$ holomorphic at infinity, the $n$-th diagonal Pad\'e
approximant to $f$, denoted by $[n/n]_f$, is a rational function of type
$(n,n)$ that has the highest order of contact with $f$ at infinity. Nuttall's
theorem provides an asymptotic formula for the error of approximation
$f-[n/n]_f$ in the case where $f$ is the Cauchy integral of a smooth density
with respect to the arcsine distribution on [-1,1]. In this note, Nuttall's
theorem is extended to Cauchy integrals of analytic densities on the so-called
algebraic S-contours (in the sense of Nuttall and Stahl).
