pole residue

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• 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

• Pole (complex analysis) — The absolute value of the Gamma function. This shows that a function becomes infinite at the poles (left). On the right, the Gamma function does not have poles, it just increases quickly. In the mathematical field of complex analysis, a pole of a …   Wikipedia

• Poincaré residue — In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of a number of such possible extensions.The theory assumes… …   Wikipedia

• Methods of contour integration — Not to be confused with Line integral. In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.[1][2][3] Contour integration is closely related to the… …   Wikipedia

• Argument principle — In complex analysis, the Argument principle (or Cauchy s argument principle) states that if f ( z ) is a meromorphic function inside and on some closed contour C , with f having no zeros or poles on C , then the following formula holds: oint {C}… …   Wikipedia

• protein — proteinaceous /proh tee nay sheuhs, tee i nay /, proteinic, proteinous, adj. /proh teen, tee in/, n. 1. Biochem. any of numerous, highly varied organic molecules constituting a large portion of the mass of every life form and necessary in the… …   Universalium

• Laurent series — A Laurent series is defined with respect to a particular point c and a path of integration γ. The path of integration must lie in an annulus (shown here in red) inside of which f(z) is holomorphic (analytic). In mathematics, the Laurent series of …   Wikipedia

• Class number formula — In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function Contents 1 General statement of the class number formula 2 Galois extensions of the rationals 3 A …   Wikipedia

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• Logarithmic derivative — In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where f ′ is the derivative of f. When f is a function f(x) of a real variable x, and takes real, strictly… …   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