residue of a function

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• Residue — may refer to: * Residue (chemistry), material remaining after a distillation or an evaporation, or portion of a larger molecule * Residue (law), portion of the testator s estate that is not specifically devised to someone in the will * Residue… …   Wikipedia

• Residue (complex analysis) — In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities. (More generally, residues can be calculated for… …   Wikipedia

• Residue theorem — The residue theorem in complex analysis is a powerful tool to evaluate line integrals of analytic functions over closed curves and can often be used to compute real integrals as well. It generalizes the Cauchy integral theorem and Cauchy s… …   Wikipedia

• Residue field — In mathematics, the residue field is a basic construction in commutative algebra. If R is a commutative ring and m is a maximal ideal, then the residue field is the quotient ring k = R / m , which is a field. Frequently, R is a local ring and m… …   Wikipedia

• residue — /rez i dooh , dyooh /, n. 1. something that remains after a part is removed, disposed of, or used; remainder; rest; remnant. 2. Chem. a. residuum (def. 2). b. an atom or group of atoms considered as a group or part of a molecule. c. that part… …   Universalium

• Doubly-periodic function — In mathematics, a doubly periodic function is a function f defined at all points z in a plane and having two periods , which are linearly independent vectors u and v such that:f(z) = f(z + u) = f(z + v).,The doubly periodic function is thus a two …   Wikipedia

• Doubly periodic function — In mathematics, a doubly periodic function is a function defined at all points on the complex plane and having two periods , which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v… …   Wikipedia

• Quadratic residue — In number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract… …   Wikipedia

• Gamma function — For the gamma function of ordinals, see Veblen function. The gamma function along part of the real axis In mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its… …   Wikipedia

• Dedekind zeta function — In mathematics, the Dedekind zeta function of an algebraic number field K, generally denoted ζK(s), is a generalization of the Riemann zeta function which is obtained by specializing to the case where K is the rational numbers Q. In particular,… …   Wikipedia

• Norm residue isomorphism theorem — In the mathematical field of algebraic K theory, the norm residue isomorphism theorem is a long sought result whose complete proof was announced in 2009. It previously was known as the Bloch–Kato conjecture, after Spencer Bloch and Kazuya Kato,… …   Wikipedia