Simultaneous Rational Approximants for a Pair of Functions with Smooth Maclaurin Series Coefficients Original Research Article

Let f(z) = Σ∞j = 0ajzj and g(z) = Σ∞j = 0bjzj be formal power series for which the quantities aj + 1aj − 1/a2j and (bj/bj + 1)/(aj/aj + 1) have a prescribed asymptotic behaviour as j → ∞. We obtain the asymptotic behaviour as l → ∞ of the (l − s, r, s), l, r, s ∈ N, Hennite-Padé approximant to (f, g) and the associated determinants.