Polynomial Approximation and Growth of Generalized Axisymmetrig Potentials

Generalized axisymmetric potentials F α (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 P n (α, α) (ξ) of degree n with parameter α as Fourier series (1.4)

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