the theory of spherical and ellipsoidal harmonics

a₁ absolutely convergent B₁ bounded variation coefficients converges to zero converges uniformly cosh ŋ Crelle's Journal denotes differential equation EXPRESSIONS FOR Pm F₁ finite formula function f given h₁ harmonic of degree hence hypergeometric series II n interval Kugelfunctionen Laplace's equation Legendre's equation Math negative number of zeros obtained P₁ P₁m P₂ µ P₂-m P₂m µ phase Pm cosh Pm µ Pn µ Pn+1 polynomial positive integer potential function Q₂m µ Qn µ real axis right-hand side satisfied shew shewn sin² sinh sinm solid harmonic spherical harmonic surface harmonics term vanish αμ αμε μ μ µ² π π