Some new class of multiple orthogonal polynomials

Abstract

Multiple orthogonal polynomials are a generalization of orthogonal polynomials in the sense that they satisfy orthogonality conditions with respect to r ∈ N different weight functions simultaneously. Here, we present multiple orthogonal polynomials that satisfy orthogonality conditions with respect to the set of r bilinear forms defined on the linear space of algebraic polynomials [1], as well as on the linear space of trigonometric polynomials, with special attention to even weight functions. These bilinear forms naturally arise in the construction of sets of anti-Gaussian quadrature rules for the optimal sets of quadrature rules in Borges’ sense on the mentioned spaces.