convergent of a continued fraction

См. также в других словарях:

• Continued fraction — Finite continued fraction, where a0 is an integer, any other ai are positive integers, and n is a non negative integer. In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the… …   Wikipedia

• Convergent (continued fraction) — A convergent is one of a sequence of values obtained by evaluating successive truncations of a continued fraction. The nth convergent is also known as the nth approximant of a continued fraction.[1] Contents 1 Representation of real numbers 2… …   Wikipedia

• Continued fraction of Gauss — In complex analysis, the continued fraction of Gauss is a particular continued fraction derived from the hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several… …   Wikipedia

• Generalized continued fraction — In analysis, a generalized continued fraction is a generalization of regular continued fractions in canonical form in which the partial numerators and the partial denominators can assume arbitrary real or complex values.A generalized continued… …   Wikipedia

• Euler's continued fraction formula — In the analytic theory of continued fractions, Euler s continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple… …   Wikipedia

• Gauss's continued fraction — In complex analysis, Gauss s continued fraction is a particular class of continued fractions derived from hypergeometric functions. It was one of the first analytic continued fractions known to mathematics, and it can be used to represent several …   Wikipedia

• convergent — 1. adjective a) That converges or focuses b) A sequence in a metric space with metric d is convergent to a point , denoted as , if for every there is a natural number N such that for every : . 2. noun the rational number obtained when a …   Wiktionary

• Solving quadratic equations with continued fractions — In mathematics, a quadratic equation is a polynomial equation of the second degree. The general form is:ax^2+bx+c=0,,!where a ne; 0.Students and teachers all over the world are familiar with the quadratic formula that can be derived by completing …   Wikipedia

• Convergence problem — In the analytic theory of continued fractions, the convergence problem is the determination of conditions on the partial numerators ai and partial denominators bi that are sufficient to guarantee the convergence of the continued fraction This… …   Wikipedia

• 239 (number) — 239 (two hundred [and] thirty nine) is the natural number following 238 and preceding 240.In mathematicsIt is a prime number. The next is 241, with which it forms a pair of twin primes. 239 is a Sophie Germain prime and a Newman Shanks Williams… …   Wikipedia

• Methods of computing square roots — There are several methods for calculating the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below. Contents 1 Rough estimation 2 Babylonian method 2.1 Example …   Wikipedia