Polynomial Approximation and Growth of Generalized Axisymmetrig Potentials

Abstract

Generalized axisymmetric potentials Fα (GASP) are regular solutions to the generalized axisymmetric potential equation(1.1)in some neighborhood Ω of the origin where they are subject to the initial data(1.2)along the singular line y = 0. In Ω, these potentials may be uniquely expanded in terms of the complete set of normalized ultraspherical polynomials(1.3)defined from the symmetric Jacobi polynomials Pn(α, α)(ξ) of degree n with parameter α as Fourier series(1.4)