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

Lemma. Let f(z) be a holomorphic function. Assume that x 0 2R is a pole of f, of order 1, with Res z=x 0 (f(z)) = B2C. Let r( ) = x 0 + rei , 0 ˇ. Thus, r is the counterclockwise semicircle of radius …

2025年3月5日 · Jordan's lemma shows the value of the integral I=int_(-infty)^inftyf(x)e^(iax)dx (1) along the infinite upper semicircle and with a>0 is 0 for "nice" functions which satisfy lim_(R …

2017年5月18日 · Physics 2400 Jordan’s Lemma Spring 2017 Jordans Lemma extends this result for a special form of g(z), g(z) = f(z)ei z; >0; (5) from functions satisfying f(z) = O 1 jzj2 to any …

Jordan’s Lemma −R.H+ R −→ Jordan’s Lemma deals with the problem of how a contour integral behaves on the semi-circular arc H+ R of a closed contour C. Lemma 1 (Jordan) If the only …

2024年4月30日 · Let r> 0 r> 0 be a real number. Let g: Cr → C g: C r → C be a continuous function. for each z ∈ Cr z ∈ C r, for some real number a> 0 a> 0. This entry was named for …

2024年2月25日 · PHYS 2400 Jordan’s Lemma Spring semester 2024 where is a real parameter, λ>0, from functions F(z) satisfying f(z) ∼1 |z|2 as |z|→∞to functions f(z) satisfying f(z) →0 as …

2020年6月5日 · Jordan's lemma can be applied to residues not only under the condition $ zf ( z) \rightarrow 0 $, but even when $ f ( z) \rightarrow 0 $ uniformly on a sequence of semi-circles …

2021年6月9日 · In quantum computing protocols, jordan's lemma keeps cropping up. See, for example, here: https://cims.nyu.edu/~regev/teaching/quantum_fall_2005/ln/qma.pdf. For any …

Jordan's Lemma is a mathematical result used in complex analysis to evaluate certain types of integrals, particularly those involving contour integration around poles. This lemma helps …