QD-algorithms and recurrence relations for biorthogonal polynomials

Biorthogonal polynomials $P^{(i,j)}_{n}$ include as particular cases vector orthogonal polynomials of dimension $d$ and $-d(d\in N)$. We pay special attention to the cases of dimension 1 and -1. We discuss the problem of computing $P^{(i,j)}_{n}$ using only one of several recurrence relations. Furthermore, we deduce all recurrence relations of a certain type that give $P^{(i,j)}_{n}$ from two others biorthogonal polynomials. the coefficient that appear in any two independents relations satisfy same identities from which it is possible to establish QD-like algorithms.