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

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.