In mathematics, the multiple orthogonal polynomials (MOPs) are orthogonal polynomials in one variable that are orthogonal with respect to a finite family of measures.
The polynomials are divided into two classes named type 1 and type 2.
[1] In the literature, MOPs are also called
-orthogonal polynomials, Hermite-Padé polynomials or polyorthogonal polynomials.
MOPs should not be confused with multivariate orthogonal polynomials.
Consider a multiindex
positive measures
μ
μ
over the reals.
As usual
are of type 1 if the
has at most degree
such that and This defines a system of
equations for the
coefficients of the polynomials
A monic polynomial
is of type 2 if it has degree
out, we get the following definition