## Continued Fractions: Lectures Given Summer 1957 at Numerical Analysis Research, Dept. of Mathematics, University of California |

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a2aU a2v+l Amer approximation error associated continued fraction av-l binomial series Cl C2 common root Consequently continued fraction 1.1 continued fraction converges continued fraction diverges continued fraction expansions continued fraction theory convergent continued fraction D. H. Lehmer different from zero elements equal equations equivalence transformation equivalent continued fraction euclidean algorithm Euler example factor following theorem holds formulas 3.3 Gauss infinite continued fraction irrational Macon Math meaningless approximants method Nathaniel Macon necessary and sufficient negative real number of terms numerators and denominators Numerical Analysis obtains partial denominator partial fraction partial numerators different Perron 28 polynomials Pringsheim rational function reciprocal value recurrence formulas recurrence relations regular C-fractions regular continued fraction sequence of approximants series converges series diverges Taylor's series theory of continued uniquely determined vanish Vl Vl wider sense writes