The Definiteness of Filippi’s Quadrature Formulae and Related Problems

Abstract

Consider a quadrature formula of order k on a finite interval normalized as

$$\begin{array}{*{20}{c}} {\int\limits_{ - 1}^1 {f\left( x \right)dx = \sum\limits_{v = 1}^n {{A_\nu }f\left( {{x_v}} \right) + {R_n}\left( f \right)} } } \\ {\left( { - 1 \leqslant {x_1} < {x_2} < \ldots < {x_{n - 1}} < {x_n} \leqslant 1} \right).} \end{array}$$

((1))

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