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An Analytical Solution Of The Laplace Equation With Robin Conditions By Applying Legendre Transform

2016
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Zenodo
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We derived the analytical solution of the Laplace equation with Robin conditions on a sphere with azimuthal symmetry by applying Legendre transform, which was expressed in terms of the Appell hypergeometric function. \( \Delta\)u=0 in a unit sphere ∂u(r, \(\zeta\))/∂r|r=1 + h u(1, \(\zeta\))= f(\(\zeta\)) on a unit sphere, \(\zeta\) = cos (\(\theta\)), \(\theta\) is the azimuthal angle, and h \(\in \textbf{R} ^{*}_{+}\) The function f(\(\theta\)) is a prescribed function and is assumed to be a

doi:10.5281/zenodo.439037
fatcat:rkrglq6y7vfeflu3jinx4dcv2m