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Polynomial Approximation and Growth of Generalized Axisymmetrig Potentials

Published online by Cambridge University Press:  20 November 2018

Peter A. McCoy
Peter A. McCoy*
Affiliation:
United States Naval Academy, Annapolis, Maryland 21402
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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)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 49 - 59
Copyright
Copyright © Canadian Mathematical Society 1979

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