What is the symbol behind the integration means in logarithmic potential ? Let's say $$x_{\mu}(z)=\int_D \ln|z-\xi|d\mu(\xi)$$ What does $\xi$ means ? I have been studying harmonic moment and I come across this term.
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$\xi$ (the Greek letter "xi") is just the integration variable. You might as well rename it $w$ if you like...
Lukas Geyer
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Then how to integrate the integral above if we integrate w.r.t. $\xi$ ? Treat the integrand as constant ? – hong wai Dec 10 '12 at 23:55
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No, it is not constant, it is the function $\xi \mapsto \ln |z-\xi|$. You can only explicitly integrate this if you know what measure $\mu$ is. – Lukas Geyer Dec 11 '12 at 00:00
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but isn't the function is $z \rightarrow ln|z-\xi|$ ? as the LHS bracket is z – hong wai Dec 11 '12 at 00:10
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$z$ is a parameter in the integral, so the result of the integration depends on $z$, and is the logarithmic potential of $\mu$ evaluated at $z$. – Lukas Geyer Dec 11 '12 at 15:35