Let v(w,y) = 8x^3y + 8ry^3 + sin(€)sinh(y). Show that v(w,y) is harmonic and find the most general holomorphic function with imaginary part v(c,y). For full marks, write f as a function of z.
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A function is harmonic if it satisfies Laplace's equation, which states that the sum of the second partial derivatives with respect to each variable is zero. In this case, we have v(w,y) = 8x^3y + 8ry^3 + sin(€)sinh(y). To show that it is harmonic, we need to Show more…
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