Results 151 to 160 of about 909 (183)

The Zeros of Certain Jacobi Polynomials

SIAM Journal on Mathematical Analysis, 1982
Two theorems are proved about the zeros of certain Jacobi polynomials that are important in the theory of interpolation and approximation.THEOREM 1. Let$S_k $and$\bar S_k $be the sums of thekth powers of the zeros of$P_n^{(w, - w)} (x)$and$P_n^{(w, - w)} ( - x)$respectively (wreal, $0 < w < 1$). Then for$k = 1,2, \cdots ,2n,S_k - \bar S_k = - 2w$ (kodd)
Young, Andrew, Hamideh, Hassan
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On Jacobi polynomials

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
1. The object of this paper is to prove some formulae of Jacobi polynomials including a generating function. The results (2·l)–(2·4), (2·6)–(2·9), (3·l)–(3·4), and (4·1) are believed to be new.
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A REMARK ON JACOBI POLYNOMIAL ESTIMATES

International Journal of Wavelets, Multiresolution and Information Processing, 2009
In this paper, an estimate of Jacobi polynomials with complex indices is proved. It improves a corresponding result of Ref. 2.
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Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients

Mathematical Proceedings of the Cambridge Philosophical Society, 1971
The answers to many important questions in the harmonic analysis of orthogonal polynomials are known to depend on the determination of when formulas of the typesand their dualshold, where pn(x) and qn(x) are suitably normalized orthogonal polynomials or orthogonal polynomials multiplied by certain functions; e.g. e−pxLn(x).
Askey, R., Gasper, G.
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A Generating Function for Jacobi Polynomials

Canadian Mathematical Bulletin, 1966
The following notations will be employed throughout this note.The object of the present note is to obtain a new generating function for the Jacobi polynomials defined by [4, page 268]
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Asymptotics of generalized jacobi polynomials

Constructive Approximation, 1986
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On the zeros of subrange Jacobi polynomials

Numerical Algorithms, 2017
All positive zeros of subrange Jacobi polynomials, orthogonal on [−c, c], 0 < c − 1, β > − 1, are shown in the ultraspherical case α = β, and partly conjectured in the general case α < β, to be monotonically increasing as functions of c.
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Sub-range Jacobi polynomials

Numerical Algorithms, 2012
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A family of generalized Jacobi polynomials

Mathematics of Computation, 1989
The family of orthogonal polynomials corresponding to a generalized Jacobi weight function was considered by Wheeler and Gautschi who derived recurrence relations, both for the related Chebyshev moments and for the associated orthogonal polynomials. We obtain an explicit representation of these polynomials, from which the recurrence relation can be ...
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Linearization of the Product of Jacobi Polynomials. II

Canadian Journal of Mathematics, 1970
Let [3, p. 170, (16)](1.1)denote the Jacobi polynomial of order (α, β), α, β > – 1, and let g(k, m, n; α, β) be denned by(1.2)where Rn(α, β)(x) = Pn(α, β)(x)/Pn(α, β)(1). It is well known [1; 2; 4; 5; 6] that the harmonic analysis of Jacobi polynomials depends, at crucial points, on the answers to the following two questions.Question 1. For which (α,
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