Ux = (∂U/∂r)(∂r/∂x) + (∂U/∂θ)(∂θ/∂x)
where r = √(x2+y2), θ = arctan (y/x), x = r cos θ, y = r sin θ. We get
Ux = (cos θ) Ur – (1/r)(sin θ) Uθ , Uxx = [∂(Ux)/∂r] (∂r/∂x) + [∂(Ux)/∂θ](∂θ/∂x)
Carry out this computation, as well as that for Uyy. Since Uxx and Uyy are both expressed in polar coordinates, their sum gives Laplace in polar coordinates.
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