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- Argument_principle abstract "In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.Specifically, if f(z) is a meromorphic function inside and on some closed contour C, and f has no zeros or poles on C, then where N and P denote respectively the number of zeros and poles of f(z) inside the contour C, with each zero and pole counted as many times as its multiplicity and order, respectively, indicate. This statement of the theorem assumes that the contour C is simple, that is, without self-intersections, and that it is oriented counter-clockwise.More generally, suppose that f(z) is a meromorphic function on an open set Ω in the complex plane and that C is a closed curve in Ω which avoids all zeros and poles of f and is contractible to a point inside Ω. For each point z ∈ Ω, let n(C,z) be the winding number of C around z. Thenwhere the first summation is over all zeros a of f counted with their multiplicities, and the second summation is over the poles b of f counted with their orders.".
- Argument_principle thumbnail Argument_principle1.svg?width=300.
- Argument_principle wikiPageID "1138322".
- Argument_principle wikiPageRevisionID "597221666".
- Argument_principle hasPhotoCollection Argument_principle.
- Argument_principle subject Category:Complex_analysis.
- Argument_principle subject Category:Theorems_in_complex_analysis.
- Argument_principle type Abstraction100002137.
- Argument_principle type Communication100033020.
- Argument_principle type Message106598915.
- Argument_principle type Proposition106750804.
- Argument_principle type Statement106722453.
- Argument_principle type Theorem106752293.
- Argument_principle type TheoremsInComplexAnalysis.
- Argument_principle comment "In complex analysis, the argument principle (or Cauchy's argument principle) relates the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.Specifically, if f(z) is a meromorphic function inside and on some closed contour C, and f has no zeros or poles on C, then where N and P denote respectively the number of zeros and poles of f(z) inside the contour C, with each zero and pole counted as many times as its multiplicity and order, respectively, indicate. ".
- Argument_principle label "Argument principle".
- Argument_principle label "Principe de l'argument".
- Argument_principle label "Principio del argumento".
- Argument_principle label "Принцип аргумента".
- Argument_principle label "辐角原理".
- Argument_principle sameAs Principio_del_argumento.
- Argument_principle sameAs Principe_de_l'argument.
- Argument_principle sameAs 편각_원리.
- Argument_principle sameAs m.049lv3.
- Argument_principle sameAs Q1370201.
- Argument_principle sameAs Q1370201.
- Argument_principle sameAs Argument_principle.
- Argument_principle wasDerivedFrom Argument_principle?oldid=597221666.
- Argument_principle depiction Argument_principle1.svg.
- Argument_principle isPrimaryTopicOf Argument_principle.