<i>t</i> -sion of Two Polynomial Sequences and Factorization Properties

Certain second-order recurrence sequences (Gn) and (Hn) give the coefficients for sequences P and Q of polynomials in ℝ[x]. The t-sion of P and Q, denoted by P ot Q, is then defined so as to generalize both the fusion and fission of P and Q. Specifically, P ot Q is the fusion of P and Q if t = 1 and the fission if t = -1. Choosing Q in a certain manner derived from P gives a sequence for which is the self t-sion of P. Explicit formulas are obtained for the polynomials in .