ultraspherical polynomials

ultraspherical polynomials

[¦əl·trə′sfer·ə·kəl ‚päl·i′nō·mē·əlz]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In [13] Olver and Townsend presented a fast spectral method for solving linear differential equations using bases of ultraspherical polynomials, which has subsequently been exploited in Chebfun [6] and ApproxFun [12].
The ultraspherical polynomials have received considerable attention in recent decades, from both theoretical and practical points of view (see, e.g., [14]).
Some Properties of Ultraspherical Polynomials and Their Shifted Ones.
It should be noted here that the ultraspherical polynomials [C.sup.([lambda]).sub.n](x) are normalized such that [C.sup.([lambda]).sub.n](1) = 1.
An extension of (1.1) to ultraspherical polynomials [P.sup.([lambda]).sub.n] [P.sup.([lambda]-1/2, [lambda]-1/2).sub.n], 0 < [lambda] < 1, is due to Lorch [6], and a further extension to Jacobi polynomials [P.sup.([alpha], [beta].sub.n]) with [absolute value of [alpha]] [less than or equal to] 1/2, [absolute value of [beta]] [less than or equal to] 1/2 to Baratella [2].
LORCH, Inequalities for ultraspherical polynomials and the gamma function, J.
ISMAIL, A generalization of ultraspherical polynomials, in Studies in Pure Mathematics, P.
BALAZS, Weighted (0, 2) -interpolation on the zeros of the ultraspherical polynomials, (in Hungarian: Sulyozott (0, 2)-interpolacio ultraszferikus polinom gyokein), MTA IILoszt.
TER AN, Notes on Interpolation I, On some interpolatorical properties of the ultraspherical polynomials, Acta Math.
[14] --, Zeros of ultraspherical polynomials and the Hilbert-Klein formulas, J.
Ultraspherical polynomials are solutions of the differential equations [L.sub.[alpha]] [p.sup.([alpha]).sub.n] = n(n + 2[alpha] + 1)[p.sup.([alpha]).sub.n], for n [member of] [N.sub.0] , where the Laplace operator is defined as