contour integral
31Matsubara frequency — In thermal quantum field theory, the Matsubara frequency summation is the summation over discrete imaginary frequency. It takes the following form , where the imaginary frequency ω is usually taken from either of the following two sets (with ) …
32Unicode-Block Mathematische Operatoren — Der Unicode Block Mathematical Operators (Mathematische Operatoren) (2200–22FF) enthält verschiedene in mathematischen Texten verwendete Zeichen, vor allem Symbole mathematischer Operatoren, unter anderem aus dem Bereich der Mengenlehre und der… …
33Beta function — This article is about Euler beta function. For other uses, see Beta function (disambiguation). In mathematics, the beta function, also called the Euler integral of the first kind, is a special function defined by for The beta function was studied …
34Знак интеграла — Не следует путать с ʃ. ∫ Знак интеграла используется для обозначения интеграла в математике. Впервые он был использован немецким математиком и основателем дифференциального и интегрального исчислений Лейбницем в конце XVII века. Символ (∫)… …
35Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …
36Estimation lemma — In mathematics, the estimation lemma gives an upper bound for a contour integral. If f is a complex valued, continuous function on the contour Gamma and if its absolute value | f ( z )| is bounded by a constant M for all z on Gamma, then:left|int …
37Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …
38Planck's law — For a general introduction, see black body. In physics, Planck s law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at temperature T. As a function of frequency u, Planck s law is written as:… …
39Jordan's lemma — in complex analysis is a powerful tool used frequently when evaluating contour integrals, and real integrals from ∞ to +∞.Consider a function of the form: ::f(z)=e^{iaz} g(z),Jordan s Lemma states that::lim {R o infty} int {C 1} f(z), dz = 0 quad …
40Laguerre polynomials — In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 ndash; 1886), are the canonical solutions of Laguerre s equation::x,y + (1 x),y + n,y = 0,which is a second order linear differential equation.This equation has… …
