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0(xnm+n+m+1 abstract Pad6 approximant abstract polynomials approximant for F Banach space boundary value problems bounded linear operator bounded operator c.F+d calculate Chebyshev coefficients commutative Banach algebra Consider continued fraction convergent couple of abstract covariance property D(Tt defined denote differential e-algorithm Edited F(xq formulas Halley Halley-iteration Halley's method Hm+1 homogeneous system integral equation inverse element irreducible form iterationsteps iterative procedure k-linear lemma Let F linear space llxll matrix method multilinear operators multiplication multivariate Pad6 approximants neighbourhood Newton Newton-correction nilpotent elements nm+j nm+m nm+n nm+n+m+1 nonlinear equations nonlinear operator normalized n,m normed numerical numerical stability operator F Pad6 approximation problem Pad6 table Pad6-approximant for F Pade Proceedings Proof prove pseudo-degree rational approximations rational operator regular sin(xy solution of 1.3.1 systems of equations Taylor series theorem Theory U D(Q univariate Pad6 approximants vector write