Results 231 to 240 of about 535,269 (286)

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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Refined multilayered beam, plate and shell elements based on Jacobi polynomials

Composite structures, 2022
E. Carrera, R. Augello, A. Pagani, D. Scano   +3 more
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Asymptotics of generalized jacobi polynomials

Constructive Approximation, 1986
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On the zeros of Jacobi polynomials

Acta Mathematica Hungarica, 1994
For \(\alpha>-1\), \(\beta>-1\), let \(x_{ni}= x_{ni} (\alpha, \beta)\) denote the \(i\)-th zero, in decreasing order, of the Jacobi polynomial \(P_ n^{(\alpha, \beta)} (x)\): \[ 1> x_{n1}> x_{n2}> \dots >x_{nn} >-1. \] Here the authors present a procedure based on the Sturm comparison theorem to obtain the following main result for \(x_{ni}\). For \(i=
Elbert, Á., Laforgia, A., Rodonó, Lucia G.   +2 more
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Accurate Computations with Collocation and Wronskian Matrices of Jacobi Polynomials

Journal of Scientific Computing, 2021
E. Mainar, Juan Manuel Peña, B. Rubio
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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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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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Trajectories of Quadratic Differentials for Jacobi Polynomials with Complex Parameters

, 2015
Motivated by the study of the asymptotic behavior of Jacobi polynomials $$\left( P_{n}^{(nA,nB)}\right) _{n}$$Pn(nA,nB)n with $$A\in \mathbb {C}$$A∈C and $$B>0$$B>0, we establish the global structure of trajectories of the related rational quadratic ...
A. Martínez-Finkelshtein, P. Martínez-González, Faouzi Thabet   +2 more
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Cari��ena polynomials are Jacobi polynomials

2009
first ...
Vignat, C., Lamberti, P. W.
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