Factorizations and representations of binary polynomial recurrences by matrix methods. (English) Zbl 1221.11033
As a generalization of second order recurrence sequences, the authors define the polynomials
\[
A_{n+1}(x)=p(x)A_n(x)+q(x)A_{n-1}(x),
\]
with initial conditions \(A_0(x)=a(x)\) and \(A_1(x)=b(x)\), where \(a,b,p,q\) are given real polynomials.
Recurrences, tridiagonal determinantal matrix representations and factorizations are given.
Recurrences, tridiagonal determinantal matrix representations and factorizations are given.
Reviewer: István Mező (Debrecen)
MSC:
11B37 | Recurrences |
11C20 | Matrices, determinants in number theory |
11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |