NEW QUADRATURE-FORMULAS BASED ON THE ZEROS OF JACOBI-POLYNOMIALS

Authors
Citation
Ak. Varma et E. Landau, NEW QUADRATURE-FORMULAS BASED ON THE ZEROS OF JACOBI-POLYNOMIALS, Computers & mathematics with applications, 30(3-6), 1995, pp. 213-220
Citations number
5
Categorie Soggetti
Computer Sciences",Mathematics,"Computer Science Interdisciplinary Applications
ISSN journal
08981221
Volume
30
Issue
3-6
Year of publication
1995
Pages
213 - 220
Database
ISI
SICI code
0898-1221(1995)30:3-6<213:NQBOTZ>2.0.ZU;2-A
Abstract
The main object of this paper is to construct a new quadrature formula based on the zeros of the polynomial (1 - x(2))P-n((alpha,beta))(x)P- n((alpha,beta)') (x), where P-n((alpha,beta)) (x) is the Jacobi polyno mial of degree n. It is interesting to mention that this quadrature fo rmula is closely related to the well-known Gaussian Quadrature formula , and above all the coefficients are also nonnegative. Thus, the quadr ature formula stated in Theorem 1 converges to integral(-1)(1) f(x)(1 - x)(alpha)(1 + x)(beta) dx.