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- Thread starter touqra
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mjsd

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describing the loop: first bit is the original bit the flat/horizontal (-R,+R) bit with R eventually taken to infinity, then to complete the loop you need to add a 1/4 of an arc going from +R to +iR, then comes down to avoid the branch cut, go around the pole and goes up again before arch back from +iR to -R.

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Why would the arc or circular bit dies away as the variable goes infinity?

describing the loop: first bit is the original bit the flat/horizontal (-R,+R) bit with R eventually taken to infinity, then to complete the loop you need to add a 1/4 of an arc going from +R to +iR, then comes down to avoid the branch cut, go around the pole and goes up again before arch back from +iR to -R.

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mjsd

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I looked up on Jordan's lemma, and yeah the integrand of the semicircular path (excluding the real axis) tends to zero as R goes infinity.

OOOooo contour integrals are so interesting !

Thank you!

Is ML estimate maximum likelihood estimate? How can ML estimate be used here since it is about probability?

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mjsd

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Suppose C is a piecewise smooth curve. If [tex]h(z)[/tex] is continuous function on C then

[tex]\displaystyle{\left|\int_{C} h(z)\, dz\right| \leq

\int_{C}|h(z)|\, |dz|}.[/tex]

and if C has length L and [tex]|h(z)|\leq M[/tex] on C then

[tex]\displaystyle{\left|\int_{C} h(z)\, dz\right| \leq ML}[/tex]

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