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Harmonic functions
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiablefunctionf:U→R{\displaystyle f\colon U\to \mathbb {R} }, where U{\displaystyle U} is an open subset of Rn{\displaystyle \mathbb {R} ^{n}}, that satisfies Laplace's equation, that is, ∂2f∂x12+∂2f∂x22+⋯+∂2f∂xn2=0{\displaystyle {\frac {\partial ^{2}f}{\partial x_{1}^{2}}}+{\frac {\partial ^{2}f}{\partial x_{2}^{2}}}+\cdots +{\frac {\partial ^{2}f}{\partial x_{n}^{2}}}=0} everywhere on U{\displaystyle U}.
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