Verify that the given function u is harmonic. u(x, y) = 8xy3 - 8x³y + x The function u(x, y) has the following second order partial derivatives. a²u = 0x² 0²u ay² 8²u Thus + and the function is harmonic. 0x² əy² Find v, the harmonic conjugate function of u. (Give your answer in terms of an arbitrary constant C.) v(x, y) = Form the corresponding analytic function f(2)= u + iv. f(x + y) =

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