On the convergence of closed interpolatory integration rules based on the zeros of Gegenbauer polynomials

摘要

The Gegenbauer polynomials Cnμ(x) are orthogonal with respect to the weight function (1 − x2)μ − 12. It is known that the interpolatory integration rules based on the zeros of (1 −x2)Cn−2μ(x) converge for all Riemann-integrable functions for 12 ⩽ μ ⩽ 4. This is shown to hold also for − 12 < μ < 12.