## Padé-type approximation and general orthogonal polynomials |

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### Contents

Introduction | 7 |

General orthogonal polynomials | 40 |

Pade approximants and related matters | 126 |

Copyright | |

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### Common terms and phrases

algorithm applying arbitrary Brezinski characteristic polynomial Christoffel-Darboux relation Ck+1 coefficients compute recursively conjugate gradient method consecutive zeros construct continued fraction convergence Corollary cross rule defined denominator denoted different from zero e-algorithm eigenvalues equal equations family of orthogonal FNTER Gaussian quadrature Hankel determinants Hermite interpolation identical infinite matrix interpolation polynomial Lemma Let us assume mants Math matrix mials minimal polynomial monic Moreover Multiplying necessary and sufficient nondecreasing numerator obtain orthogonal polynomials orthogonal with respect orthogonality relations Pade approximants Pade table Pade-type approximants Pk(x polyno polynomial of degree polynomial with degree polynomials Pk polynomials with respect positive definite preceding relation preceding results Proof proved rational approximation rational function recurrence relation result follows Rossum satisfied Shanks transformation sufficient condition term Theorem TM sequences topological variables vectors written Wynn zeros of Pk