Some Weighted Sums of Powers of Fibonacci Polynomials
Journal
Integers
Date Issued
2014
Author(s)
Pita-Ruiz, Claudio
Type
text::book::book part
Abstract
We obtain closed formulas for some weighted sums of powers of bivariate
Fibonacci and Lucas polynomials of the form q
n=0 λn (x, y) Fk
tsn+l (x, y) and
q
n=0 λn (x, y)Lk
tsn+l (x, y), in the cases k = 1, 2, 3, 4, and some specific values
of the parameters t and l. We express these sums as linear combinations of the
Fibopolynomials q+m
tk
Fs(x,y)
, m = 1, 2, . . . , tk.
Fibonacci and Lucas polynomials of the form q
n=0 λn (x, y) Fk
tsn+l (x, y) and
q
n=0 λn (x, y)Lk
tsn+l (x, y), in the cases k = 1, 2, 3, 4, and some specific values
of the parameters t and l. We express these sums as linear combinations of the
Fibopolynomials q+m
tk
Fs(x,y)
, m = 1, 2, . . . , tk.