Formal orthogonal polynomials and rational approximation for arbitrary bilinear forms

Classically, formal orthogonal polynomials are studied with respect to a linear functional, which gives rise to a moment matrix with a Hankel structure. Moreover, in most situations, the moment matrix is supposed to be strongly regular. This implies a number of algebraic properties which are well known, like for example the existence of a three-term recurrence relation (characterised by a tridiagonal Jacobi matrix), Pad\'e approximation properties etc. In this note we shall investigate how these formal algebraic properties generalize for moment matrices with no special structure. Subsequently, we shall look especially at the case of a moment matrix with an indefinite Hankel structure and with a nonsymmetric indefinite Toeplitz structure.nrpages: 18status: publishe