Multidimensional Padé approximation of binomial functions: equalitieswith Michael A. Bennett and Kevin O'Bryant Let ω0,...,ωM be real numbers. If H0,...,HM are polynomials of degree at most ρ0,...,ρM, and G(z) = Σ0≤m≤M Hm(z) (1-z)ωm has a zero at z=0 of maximal order (for the given ωm and ρm), we say that H0,...,HM are a multidimensional Padé approximation of binomial functions, and call G(z) the Padé remainder. We collect here with proof all of the known expressions for G and Hm, including a new one: the Taylor series of G. We also give a new criterion for systems of Padé approximations of binomial functions to be perfect (a specific sort of independence used in applications).
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