Polynomial Approximation and Growth of Generalized Axisymmetrig Potentials

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)