Valutazione dell'errore per una formula di quadratura alla Tchebycheff di tipo chiuso

In this paper we study the remainder term of a quadrature formula of the form $$\int\limits_{ - 1}^1 {f(x)dx = A_n \left {f( - 1) + f(1)} \right] + C_n \sum\limits_{i = 1}^n {f(x_{n,i} ) + R_n \left f \right],} } $$ , withx _x,i ∈^-1,1, andR _n f]=0 whenf(x) is a polynomial of degree ≤n+3 ifn is even, or ≤n+2 ifn is odd. Such a formula exists only forn=1(1)11. It is shown that, iff(x)∈ ^C(h+1) -1,1], (h=n+3 orn+2), thenR _n f]=f ^h+1 (τ)·± _n . The values α _n are given.