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The Structure of the Pade Table
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analytic function apply argument assumption asymptotic Baker block branch points Chapter circle column complex plane compute conclude consider continued fraction converges uniformly Corollary define definition derive determinant determinantal conditions entire function equicontinuous error essential singularities example factor finite number formal power series formula given goes to infinity Hence holds implies inclusion regions inequalities integral Lemma limit point linear fractional transformation mants meromorphic function multiply nonzero normalization number of poles numerator and denominator obtain origin orthogonal Pade approximants Pade approximants converge Pade denominators Pade equations Pade table Pk(z poles and zeros polynomial of degree problem Proof properties radius of convergence recursion relations region of convergence residues Riemann sphere roots satisfy scattering amplitude sequence of Pade series coefficients series expansion series of Stieltjes solution Taylor series tends to infinity tends to zero Theorem 9.1 unique vanish