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I am trying to solve the finite Hilbert transformation like the following form $ f(x)= \frac{1}{π} \int_{-1}^{1} \frac{g(y)}{(y-x)}dy $ the given function f(x)=1 and I want to solve the g(x) I know there is no direct way to solve the integral equation in Mathematica. Moreover, I found some boundary problems when solving it. Does anyone provide some useful tips?

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Possibly related: (341) -- I've closed this question until is is clarified a bit. Please do not think you are unwelcome here; rather we don't want people trying to answer the wrong question. –  Mr.Wizard Aug 13 '13 at 7:03
You can use LaTeX mark-up; see all the questions in this search for examples. This guide may help. –  Mr.Wizard Aug 13 '13 at 7:08
When it is solved analytically, it is Cauchy principal integral equation. So, I think it cannot be solved by the Fredholm theorem. –  Henry Aug 13 '13 at 8:02
Reopened as requested. –  Mr.Wizard Aug 13 '13 at 8:16

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