In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

Contour integration is closely related to the calculus of residues, a method of complex analysis. One use for contour integrals is the evaluation of integrals...

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions...

Meromorphic function Entire function Pole (complex analysis) Zero (complex analysis) Residue (complex analysis) Isolated singularity Removable singularity...

refinery Residue (chemistry), materials remaining after a physical separation process, or by-products of a chemical reaction Residue (complex analysis), complex...

In complex analysis (a branch of mathematics), a pole is a certain type of singularity of a complex-valued function of a complex variable. It is the simplest...

the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory...

Organic Residue Analysis (ORA) refers to the study of micro-remains trapped in or adhered to artifacts from the past. These organic residues can include...

In complex analysis, a branch of mathematics, the residue at infinity is a residue of a holomorphic function on an annulus having an infinite external...

Partial fraction Line integral Residue (complex analysis) Residue theorem Markushevich, A.I. Theory of functions of a complex variable. Trans. Richard A....

by a complex number of modulus 1 acts as a rotation. The complex plane is sometimes called the Argand plane or Gauss plane. In complex analysis, the complex...

That all holomorphic functions are complex analytic functions, and vice versa, is a major theorem in complex analysis. Holomorphic functions are also sometimes...

In complex analysis, Liouville's theorem, named after Joseph Liouville (although the theorem was first proven by Cauchy in 1844), states that every bounded...

Residual in a residuated lattice, loosely analogous to division Residue (complex analysis) Solow residual, in economics "Residuals" (song), a song by Chris...

most natural proofs for statements in real analysis or even number theory employ techniques from complex analysis (see prime number theorem for an example)...

In complex analysis, a branch of mathematics, Morera's theorem, named after Giacinto Morera, gives a criterion for proving that a function is holomorphic...

In complex analysis, a branch of mathematics, the antiderivative, or primitive, of a complex-valued function g is a function whose complex derivative...

Renewable Electricity Standard Renewable Energy Systems, a UK company Residue (complex analysis) function Reticuloendothelial system, in anatomy Répertoire d'Épigraphie...

In number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x...

In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of...

distinguished from complex analysis, which deals with the study of complex numbers and their functions. The theorems of real analysis rely on the properties...

formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk...

functions. In complex analysis, a function is called analytic in an open set "U" if it is (complex) differentiable at each point in "U" and its complex derivative...

In complex analysis, Jordan's lemma is a result frequently used in conjunction with the residue theorem to evaluate contour integrals and improper integrals...

important role throughout complex analysis (cf. the statement of the residue theorem). In the context of complex analysis, the winding number of a closed...

In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles...

Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important...

integrals over two separate complex variables should come to a double integral over a two-dimensional surface. This means that the residue calculus will have to...

function is meromorphic. Many important tools of complex analysis such as Laurent series and the residue theorem require that all relevant singularities...