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- Estimation_lemma abstract "In mathematics the estimation lemma, also known as the M-L inequality, gives an upper bound for a contour integral. If f is a complex-valued, continuous function on the contour and if its absolute value |f(z)| is bounded by a constant M for all z on , thenwhere is the arc length of . In particular, we may take the maximumas upper bound. Intuitively, the lemma is very simple to understand. If a contour is thought of as many smaller contour segments connected together, then there will be a maximum |f(z)| for each segment. Out of all the maximum |f(z)|'s for the segments, there will be an overall largest one. Hence, if the overall largest |f(z)| is summed over the entire path then the integral of f(z) over the path must be less than or equal to it.The estimation lemma is most commonly used as part of the methods of contour integration with the intent to show that the integral over part of a contour goes to zero as goes to infinity. An example of such a case is shown below.".
- Estimation_lemma thumbnail Upper_halfcircle_with_i.svg?width=300.
- Estimation_lemma wikiPageID "5676427".
- Estimation_lemma wikiPageRevisionID "550119681".
- Estimation_lemma hasPhotoCollection Estimation_lemma.
- Estimation_lemma subject Category:Complex_analysis.
- Estimation_lemma subject Category:Lemmas.
- Estimation_lemma type Abstraction100002137.
- Estimation_lemma type Communication100033020.
- Estimation_lemma type Lemma106751833.
- Estimation_lemma type Lemmas.
- Estimation_lemma type Message106598915.
- Estimation_lemma type Proposition106750804.
- Estimation_lemma type Statement106722453.
- Estimation_lemma comment "In mathematics the estimation lemma, also known as the M-L inequality, gives an upper bound for a contour integral. If f is a complex-valued, continuous function on the contour and if its absolute value |f(z)| is bounded by a constant M for all z on , thenwhere is the arc length of . In particular, we may take the maximumas upper bound. Intuitively, the lemma is very simple to understand.".
- Estimation_lemma label "Estimation lemma".
- Estimation_lemma label "Lemme d'estimation".
- Estimation_lemma sameAs Lemme_d'estimation.
- Estimation_lemma sameAs m.0dzkx0.
- Estimation_lemma sameAs Q3229331.
- Estimation_lemma sameAs Q3229331.
- Estimation_lemma sameAs Estimation_lemma.
- Estimation_lemma wasDerivedFrom Estimation_lemma?oldid=550119681.
- Estimation_lemma depiction Upper_halfcircle_with_i.svg.
- Estimation_lemma isPrimaryTopicOf Estimation_lemma.
