I would like to know if, given F(x,y) a real function of 2 variables that obeys $\nabla^{2} \left(F \left( x,y \right)\right) = 0$ , is it true that F(x,y) always equals its Taylor expansion within the radius of convergence of the Taylor series? Or are there more conditions that are required?
2026-03-31 09:07:19.1774948039
2D Taylor expansion of F(x,y) where F(x,y) is harmonic (a solution of Laplace equation)
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Harmonic functions are analytic, so the answer is yes.