Linearization and connection coefficients of polynomial sequences: A matrix approach

Connection and linearization coefficients of the Askey-Wilson polynomials

The linearization problem is the problem of finding the coefficients Ck (m,n) in the expansion of the product Pn(x)Qm(x) of two polynomial systems in terms of a third sequence of polynomials Rk (x), Pn(x)Qm(x) = n+m ∑ k=0 Ck (m,n)Rk (x). The polynomials Pn , Qm and Rk may belong to three different polynomial families. In the case P = Q = R, we get the (standard ) linearization or Clebsch-Gordan...

On linearization and connection coefficients for generalized Hermite polynomials

We consider the problem of finding explicit formulae, recurrence relations and sign properties for both connection and linearization coefficients for generalized Hermite polynomials. The most computations are carried out by the computer algebra system Maple using appropriate algorithms.

Linearization coefficients for Sheffer polynomial sets via lowering operators

The lowering operator σ associated with a polynomial set {P n } n≥0 is an operator not depending on n and satisfying the relation σP n = nP n−1. In this paper, we express explicitly the linearization coefficients for polynomial sets of Sheffer type using the corresponding lowering operators. We obtain some well-known results as particular cases.

Connection and Linearization Problems

A permuted factors approach for the linearization of polynomial matrices

In [1] and [2] a new family of companion forms associated to a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in [3] where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family of companion like linearizations, using products of up...