INEQUALITIES FOR ULTRASPHERICAL POLYNOMIALS AND APPLICATION TO QUADRATURE

[摘要] In this paper, for the ultraspherical polynomials P(n)(lambda), we investigate inequalities of the type (sin theta)gamma\P(n)(lambda)(cos theta)\ less-than-or-equal-to M, lambda greater-than-or-equal-to 1. Applying the results to linear functionals, we obtain new estimates, in particular, for the remainder term in Gaussian quadrature.

[发布日期] 1993-12-31

[关键词] ULTRASPHERICAL POLYNOMIALS;INEQUALITIES;GAUSSIAN QUADRATURE;PEANO CONSTANTS