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On the zeros of Jacobi polynomials

✍ Scribed by Á. Elbert; A. Laforgia; Lucia G. Rodonó

Publisher
Akadmiai Kiad
Year
1994
Tongue
English
Weight
296 KB
Volume
64
Category
Article
ISSN
1588-2632

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📜 SIMILAR VOLUMES

New quadrature formulas based on the zer
New quadrature formulas based on the zeros of Jacobi polynomials
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The main object of this paper is to construct a new quadrature formula based on the zeros of the polynomial (1 -x2)P(a'f~)(x)P(a'B)' (x), where P(a'f~)(x) is the Jacobi polynomial of degree n. It is interesting to mention that this quadrature formula is closely related to the wellknown Gaussian Quad

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The main object of this paper is to construct a Birkhoff quadrature formula of the form which is exact for the polynomials of degree < 2n + 2k + 1. We construct the formula when the nodes {Xi}; and {zt}F-' are the zeros of the ultraspherical polynomials P~k'(z) and P,$""(z), respectively.

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✍ Y.G. Shi 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 272 KB

A necessary and sufficient condition of regularity of \((0,1, \ldots, m-2, m)\)-interpolation on the zeros of the Jacobi polynomials \(P_{n}^{(x, \beta)}(x)(\alpha, \beta \geqslant-1)\) in a manageable form is established. Meanwhile, the explicit representation of the fundamental polynomials, when t