Gegenbauer polynomials

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Gegenbauer polynomials

[′gāg·ən‚bau̇r ‚päl·i′nō·mē·əlz]
(mathematics)
A family of polynomials solving a special case of the Gauss hypergeometric equation. Also known as ultraspherical polynomials.
References in periodicals archive ?
Moreover, they calculated the 0-eigenspace and the generalized 0-eigenspace of [E.sup.2] in the spheroidal coordinates, in terms of series expansion of specific combinations of particular kind of Gegenbauer functions [16, 17].
We utilised the concept of semiseparation and the R-separation and we obtained the eigenfunctions of the 0-eigenspace of [E'.sup.2] expressed as products of Gegenbauer functions divided by the Euclidian distance r, while the generalized 0-eigenspace of [E'.sup.2] consisted of combinations of products of Gegenbauer functions divided by [r.sup.3].
The 0-eigenspace of the operator [E'.sup.2] is given as R-separable solutions of Gegenbauer functions of the angular and radial dependence, with R being the Euclidian distance r, expressed in the particular coordinate system.