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partial fraction expansion

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  • Partial fraction — In algebra, the partial fraction decomposition or partial fraction expansion is a procedure used to reduce the degree of either the numerator or the denominator of a rational function (also known as a rational algebraic fraction). In symbols, one …   Wikipedia

  • Partial fractions in complex analysis — In complex analysis, a partial fraction expansion is a way of writing a meromorphic function f(z) as an infinite sum of rational functions and polynomials. When f(z) is a rational function, this reduces to the usual method of partial… …   Wikipedia

  • Partial fractions in integration — In integral calculus, the use of partial fractions is required to integrate the general rational function. Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of partial fractions. Each… …   Wikipedia

  • 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

  • Periodic continued fraction — In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form:x = a 0 + cfrac{1}{a 1 + cfrac{1}{a 2 + cfrac{ddots}{quadddotsquad a k + cfrac{1}{a {k+1} + cfrac{ddots}{quadddotsquad a {k+m 1} +… …   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

  • Engel expansion — The Engel expansion of a positive real number x is the unique non decreasing sequence of positive integers {a 1,a 2,a 3,dots} such that:x=frac{1}{a 1}+frac{1}{a 1a 2}+frac{1}{a 1a 2a 3}+cdots.;Rational numbers have a finite Engel expansion, while …   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 (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

  • 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

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