Some Identities Involving the Fibonacci Polynomials

for » = (>, 1,2,.... If x = 1, then the sequence F(l) is called the Fibonacci sequence, and we shall denote it by F = {F„). The various properties of {Fn) were investigated by many authors. For example, Duncan [1] and Kuipers [3] proved that QogFJ is uniformly distributed mod 1. Robbins [4] studied the Fibonacci numbers of the forms px ±1 and px ± 1, where p is a prime. The second author [5] obtained some identities involving the Fibonacci numbers. The main purpose of this paper is to study how to calculate the summation involving the Fibonacci polynomials: