Quadrature rules for periodic integrands. Bi-orthogonality and para-orthogonality ⁄

In this paper, the algebraic construction of quadrature formulas for weighted periodic integrals is revised. For this purpose, two classical papers ([10] and [14]) in the literature are revisited and certain relations and connections are brought to light. In this respect, the concepts of “bi-orthogonality” and “para-orthogonality” are shown to play a fundamental role.