“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials

Abstract

Many researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields. There are many useful identities on recurrence relation sequence but there main problem to find any term of recurrence relation sequence we need to find previous all terms of recurrence relation sequence of numbers and polynomials. There were many important theorems obtained on recurrence relation sequences. In this paper we have given special identity for generalized Fibonacci sequence of number and Fibonacci sequence of polynomials. These identities are very useful to represent Fibonacci generalized sequence of numbers and Fibonacci sequence of polynomials in the form of matrix. Authors define a special formula in this paper by this we can find special representation of Fibonacci generalized sequence of numbers and Fibonacci sequence of polynomials in the form of matrix. So, we can say that this paper is generalization of property of Fibonacci sequence of number and Fibonacci sequence of polynomials