## Fundamentals of mathematical physics |

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analytic function arbitrary axis becomes Bessel functions boundary conditions boundary curve called charge circle coefficients components compute Consider constant converges coordinate system corresponding cosh cube curl defined density derivative Dirichlet problem displacement divergence theorem dx dy eigenvalues element evaluate example expansion flux formula Fourier transform given gives gradient Green's function Hence infinite infinity initial conditions integral theorem interior interval inversion theorem Laplace transform Laplace's equation line source linear linearly independent loop matrix obtain orthogonal outward normal partial differential equations particle particular integral plane polynomial potential power series radius represents result Riemann Riemann surface satisfies Eq scissor cut side of Eq simply connected sinh ky solution of Eq solve space sphere spherical coordinates Suppose surface S(V tensor tion two-dimensional unit vanishes variable vector field volume wave equation write Wronskian zero