## Continued fractions: Lectures given Summer 1957 at Numerical Analysis Research, Dept. of Mathematics, University of California, Los Angeles |

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2v+l a2v+l ala2 Amer approximant of 1.1 approximation error binomial series C-fraction Cauchy cl c2 coefficients common root Consequently continued fraction 1.1 continued fraction converges continued fraction diverges continued fraction expansions convergent continued fraction corresponding series different from zero equivalence transformation equivalent continued fraction Euler factor following theorem holds formulas 3.3 fractionibus continuis Gauss infinite continued fraction infinite series l)-st approximant Macon Math meaningless approximants method Nathaniel Macon necessary and sufficient negative real number of terms numerators and denominators obtains partial denominator partial fraction partial numerators different Perron 28 Pringsheim rational function reciprocal value recurrence formulas recurrence relations regular continued fraction sequence of approximants series converges series diverges Taylor's series th order theory of continued uniquely determined v-th partial vanish Vl Vl volo wider sense writes