convergents

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• semi-convergent, semi-convergente, semi-convergents, semi-convergentes — ● semi convergent, semi convergente, semi convergents, semi convergentes adjectif Se dit d une série convergente qui n est pas absolument convergente …   Encyclopédie Universelle

• 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

• 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

• convergent — convergent, ente [ kɔ̃vɛrʒɑ̃, ɑ̃t ] adj. • 1611; lat. convergens → converger 1 ♦ Qui converge. Lignes convergentes. Des routes convergentes en un point. Regards convergents sur un même objet. Lentille convergente, qui fait converger les rayons… …   Encyclopédie Universelle

• 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

• 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

• Fundamental recurrence formulas — In the theory of continued fractions, the fundamental recurrence formulas relate the partial numerators and the partial denominators with the numerators and denominators of the fraction s successive convergents. Let be a general continued… …   Wikipedia

• 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

• Square root of 5 — The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. This number appears in the formula for the golden ratio. It can be denoted in surd form as::sqrt{5}.It is an irrational algebraic number.… …   Wikipedia

• Pell's equation — is any Diophantine equation of the form:x^2 ny^2=1,where n is a nonsquare integer and x and y are integers. Trivially, x = 1 and y = 0 always solve this equation. Lagrange proved that for any natural number n that is not a perfect square there… …   Wikipedia

• Complete quotient — In the metrical theory of regular continued fractions, the kth complete quotient ζ k is obtained by ignoring the first k partial denominators ai. For example, if a regular continued fraction is given by then the successive complete quotients ζ k… …   Wikipedia