The Theory of Potential and Spherical Harmonics

analytic function arbitrary assume boundary value problem bounded C₁ Chapter circle closed surface coefficients condition conformal mapping constant converges uniformly coordinates cos(n defined density differential equation Dirichlet problem double layer expansion exterior finite number follows force field Fourier series grad Green's formula Green's function harmonic of order Hence homogeneous equation infinite inside integral equation interior kernel Laplace's equation Legendre polynomials linear linearly independent lines of force logarithmic potential mass neighbourhood Newtonian potential normal derivative obtain orthogonal plane point Q potential due potential function power series prove radius regular at infinity regular harmonic function regular potential S₁ singular point solution sphere spherical harmonics surface spherical harmonic theory tion u₁ uniformly convergent V₁ valid vector zero θη ξη ди ди дх ду