A theory of spline quadrature rules for arbitrary continuity class in a closed interval $[a, b]$ with arbitrary nonuniform subintervals based on semi-classical orthogonal Jacobi polynomials is proposed. For continuity class $c \ge 2$ this theory depends on a conjecture.

翻译：提出了在以半古典正统正数多义多元分子为基础的封闭间距 $[a, b]$的任意非统一次间隔内任意连续等级的样状二次规则理论。对于连续等级 $c\ge 2$,该理论取决于一个推测。