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New quadrature formulas based on the zeros of Jacobi polynomials

โœ Scribed by A.K. Varma; E. Landau

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
364 KB
Volume
30
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

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 Quadrature formula, and above all the coefficients ave also nonnegative. Thus, the quadrature formula stated in Theorem 1 converges to .f_l 1 f(x)(1 -x)a(1 + x) f~ dx.

๐Ÿ“œ SIMILAR VOLUMES

Regularity and Explicit Representation o
Regularity and Explicit Representation of (0, 1, ..., m-2, m)-Interpolation on the Zeros of the Jacobi Polynomials
โœ Y.G. Shi ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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