## The application of continued fractions and their generalizations to problems in approximation theory |

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### Contents

Transformations of Continued Fractions | 9 |

The Transformation of Series into Continued Fractions | 23 |

General Considerations in the Convergence Theory | 31 |

Copyright | |

29 other sections not shown

### Common terms and phrases

absolute convergence according analytic function arccos arcsin arctan becomes Bessel function chapter condition 6.12 conditional convergence Consequently continued fraction 6.2 continued fraction expansion Convergence Test convergents of expansion converges throughout converges uniformly cosh Denote domain equal to zero equation 1.2 expansion 10.3 finite complex plane finite number following theorem fraction 1.1 function K(x Hence inessential divergence integral Jm(x Khovanskii Km(x Lagrange lim PnlQn mathematical induction method of Viskovatoff notation partial denominators partial numerators Perron 73 Pn-l points of inessential power series Pringsheim Pringsheim 79 Qm(x Qn Qn-2 Qn-iQn Qn-l Qn+l QnQn-l Rational Function Approximations relationships Replacing Riccati equation right hand side satisfying the inequality sinh solution of equation tan2 tanh theorem of section tinued fraction uniform convergence whence ydxk