My Python Scripts

Create, edit, and import your Python scripts

Library

My scripts

My calculator

residus.py

Created by condouarthur

Created on October 10, 2023

585 Bytes

Res(f,z0)=a-1 = 1/2ipi int sur contour f(u)du
Si z0 pole simple Res(z0)=limI(z-zo)If(z) quand z tend vers zo
aussi si f(z) = g(z)/h(z) resf(zo) = g(zo)/h'(zo)
Si zo pole d'ordre m :
  Res(f,zo)=1/(m/1)! * lim z qui tend vers zo d^m-1/dz^m-1 * I(z-zo)^m(f(z))I
théorème de Cauchy-Goursat :
  Soit f fonction holomorphe sur un rectangle R alors int sur R de f = 0
Théorème des résidus :
  Int de f sur le contour = 2ipisomme des Res de f en zoi
Lemme de Jordan : 
  Si lim r -> 0 de I(Z-zo)f(z)I = 0 alors lim R 0 de int sur gamma de f = 0
( même chose pour + inf )

During your visit to our site, NumWorks needs to install "cookies" or use other technologies to collect data about you in order to:

With the exception of Cookies essential to the operation of the site, NumWorks leaves you the choice: you can accept Cookies for audience measurement by clicking on the "Accept and continue" button, or refuse these Cookies by clicking on the "Continue without accepting" button or by continuing your browsing. You can update your choice at any time by clicking on the link "Manage my cookies" at the bottom of the page. For more information, please consult our cookies policy.

Accept and continue Continue without accepting