Finding the harmonic conjugate given real part
0
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I have $Im(z)=ln(x^2+y^2)$ and need to find the harmonic conjugate of it.
I'm looking at SO question and its answer Showing that $u(x, , y) = ln(x^2 + y^2)$ is harmonic without computing partial derivatives
The answer there is $2ln z$ but in the book I have it's $2iln z$. So what's missing?
complex-analysis harmonic-analysis
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
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add a comment |
0
$begingroup$
I have $Im(z)=ln(x^2+y^2)$ and need to find the harmonic conjugate of it.
I'm looking at SO question and its answer Showing that $u(x, , y) = ln(x^2 + y^2)$ is harmonic without computing partial derivatives
The answer there is $2ln z$ but in the book I have it's $2iln z$. So what's missing?
complex-analysis harmonic-analysis
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
$endgroup$
$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21
add a comment |
0
0
0
1
$begingroup$
I have $Im(z)=ln(x^2+y^2)$ and need to find the harmonic conjugate of it.
I'm looking at SO question and its answer Showing that $u(x, , y) = ln(x^2 + y^2)$ is harmonic without computing partial derivatives
The answer there is $2ln z$ but in the book I have it's $2iln z$. So what's missing?
complex-analysis harmonic-analysis
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
$endgroup$
I have $Im(z)=ln(x^2+y^2)$ and need to find the harmonic conjugate of it.
I'm looking at SO question and its answer Showing that $u(x, , y) = ln(x^2 + y^2)$ is harmonic without computing partial derivatives
The answer there is $2ln z$ but in the book I have it's $2iln z$. So what's missing?
complex-analysis harmonic-analysis
complex-analysis harmonic-analysis
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
edited Dec 17 '18 at 15:21
user3132457
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
asked Dec 17 '18 at 6:13
user3132457user3132457
1598
1598
$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21
add a comment |
$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21
$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21
add a comment |
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$begingroup$
$2 Log , z$ is an analytic function in $mathbb C setminus (-infty, 0]$ with real part $ln (x^{2}+y^{2})$ where Log denotes the principal branch of logarithm. I have not seen people wiring ln for principle logarithm.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 6:46
$begingroup$
In what region are you trying to find the harmonic conjugate? Your function does not have a harmonic conjugate in $mathbb Csetminus {0}$.
$endgroup$
– Kavi Rama Murthy
Dec 17 '18 at 7:17
$begingroup$
actually this is the imaginary part, sorry
$endgroup$
– user3132457
Dec 17 '18 at 15:21