Quadrature rules for $C^0$, $C^1$ splines, the real line, and the five (5) families

Abstract

The five (5) families of quadrature rules with periods of one or two intervals for the real line and spline classes $C^0$, $C^1$ are presented. The formulae allow one to calculate the points or weights of these quadrature rules in a very simple manner as for the classical Gauss-Legendre rules.