Milne-Thomson method for finding a holomorphic function

In mathematics, the Milne-Thomson method is a method of finding a holomorphic function, whose real or imaginary part is given. The method greatly simplifies the process of finding the holomorphic function whose real or imaginary or any combination of the two parts is given. It is named after Louis Melville Milne-Thomson.

Let ${\displaystyle f(z)=u(x,y)+iv(x,y)}$ be any holomorphic function.

Let ${\displaystyle z=x+iy}$ and ${\displaystyle {\bar {z}}\ =x-iy}$ where x and y are real.

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