problem with a residue at infinity The Next CEO of Stack OverflowResidue with half order pole?Contour Integrals Around a Branch CutIntegral with contour integrationCan Cauchy principal values of functions with nonsimple poles be evaluated using complex contour integration methods?Integral using Cauchy's integral formula and residue theoremIntegrating secans over the imaginary axis using the residue theoremContour integral around 'D-contour'Looking for a bound on a contour integralDe forming the contour and showing that the contributions of contours of infinitely small lengths go to zeroEvaluating a simple integral with the Cauchy residue theorem and a semicircular contour
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problem with a residue at infinity
The Next CEO of Stack OverflowResidue with half order pole?Contour Integrals Around a Branch CutIntegral with contour integrationCan Cauchy principal values of functions with nonsimple poles be evaluated using complex contour integration methods?Integral using Cauchy's integral formula and residue theoremIntegrating secans over the imaginary axis using the residue theoremContour integral around 'D-contour'Looking for a bound on a contour integralDe forming the contour and showing that the contributions of contours of infinitely small lengths go to zeroEvaluating a simple integral with the Cauchy residue theorem and a semicircular contour
$begingroup$
I have this contour integral, which is just a standard one. It has two simple poles in $z=i$ and $z=4i$ and I already worked out the result for a path that enclose both of the poles which is
$$int_gammafracz^2-1left(z-i4right)left(z-iright)dz=-10pi.$$
Now I want to obtain the same result considering a change of variable $w=1/z$ and considering a path only around zero. Heuristically everything should be ok, but I can't obtain the result.
Can anybody get the right result?
complex-analysis contour-integration
asked 2 days ago
Dac0Dac0
5,9541936
$endgroup$
add a comment |
$begingroup$
I have this contour integral, which is just a standard one. It has two simple poles in $z=i$ and $z=4i$ and I already worked out the result for a path that enclose both of the poles which is
$$int_gammafracz^2-1left(z-i4right)left(z-iright)dz=-10pi.$$
Now I want to obtain the same result considering a change of variable $w=1/z$ and considering a path only around zero. Heuristically everything should be ok, but I can't obtain the result.
Can anybody get the right result?
complex-analysis contour-integration
asked 2 days ago
Dac0Dac0
5,9541936
$endgroup$
$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday
add a comment |
$begingroup$
I have this contour integral, which is just a standard one. It has two simple poles in $z=i$ and $z=4i$ and I already worked out the result for a path that enclose both of the poles which is
$$int_gammafracz^2-1left(z-i4right)left(z-iright)dz=-10pi.$$
Now I want to obtain the same result considering a change of variable $w=1/z$ and considering a path only around zero. Heuristically everything should be ok, but I can't obtain the result.
Can anybody get the right result?
complex-analysis contour-integration
asked 2 days ago
Dac0Dac0
5,9541936
$endgroup$
I have this contour integral, which is just a standard one. It has two simple poles in $z=i$ and $z=4i$ and I already worked out the result for a path that enclose both of the poles which is
$$int_gammafracz^2-1left(z-i4right)left(z-iright)dz=-10pi.$$
Now I want to obtain the same result considering a change of variable $w=1/z$ and considering a path only around zero. Heuristically everything should be ok, but I can't obtain the result.
Can anybody get the right result?
complex-analysis contour-integration
complex-analysis contour-integration
asked 2 days ago
Dac0Dac0
5,9541936
asked 2 days ago
Dac0Dac0
5,9541936
edited 2 days ago
Dac0
asked 2 days ago
Dac0Dac0
5,9541936
asked 2 days ago
Dac0Dac0
5,9541936
asked 2 days ago
Dac0Dac0
5,9541936
5,9541936
$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday
add a comment |
$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday
$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday
$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday
add a comment |
0
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$begingroup$
ok I made a mistake and took $a_-1$ instead of $a_1$
$endgroup$
– Dac0
yesterday