## Laurent series and their Padé approximations |

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### Contents

Moebius transforms continued fractions and Pade | 11 |

Two algorithms | 29 |

All kinds of Pade Approximants | 37 |

Copyright | |

17 other sections not shown

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### Common terms and phrases

Am(z analytic asymptotic bilinear form block structure Bn(z chapter Christoffel-Darboux relations classical Pade coefficients compact subsets compute constant continued fraction corollary defined definition denominator denote described in section determinant expression diagonal dual Rutishauser polynomials equations F+(z FG parameters finite fkzk fls F(z follows formal Laurent series function as described give given in theorem Hankel matrix Hence initial conditions introduced Laurent polynomials Laurent-Pade approximants lemma Let F(z linear lower triangular meromorphic function Moebius transforms monic node nonzero normal fis notation obtain orthogonal polynomials P^Kz Pade approximation Pade table poles polynomial of degree power series previous theorem problem PROOF prove Q^Kz R^Kz recurrence relation reproducing kernel rhombus rhombus rules right hand side satisfy Schur function Similarly solution SS parameters Suppose T-table theorem Toeplitz determinants Toeplitz matrices Toeplitz operator triangular factors two-point Pade unit circle unit disc upper triangular zeros