Orthogonal polynomials of dimension –1 in the non-definite case

Abstract

Abstract: Orthogonal polynomials of dimension d = −1 are a particular case of vector orthogonal polynomials which are, themselves, a particular case of biorthogonal polynomials. In this paper, we give the three-term recurrence relationship satisfied by these polynomials in the non-definite case, that is when some of them do not exist. Orthogonal polynomials of dimension −1 generalize orthogonal polynomials on the unit circle.

Keywords

• orthogonal polynomials
• recurrence relation
• biorthogonality