Abstract
In this paper, we derive new generating functions for the products of k-Fibonacci numbers, k-Pell numbers, k-Jacobsthal numbers and the Chebychev polynomials of the second kind by making use of useful properties of the symmetric functions.
Highlights
Introduction and PreliminariesFibonacci and Lucas numbers have been studied by many researchers for a long time to get intrinsic theory and applications of these numbers in many research areas as Physics, Engineering, Architecture, Nature and Art
{ } { } k-Fibonacci Fk,n n∈ and k-Jacobsthal Jk,n n∈ sequences have been defined by the recursive equations [2,3];
The main purpose of this paper is to present some results involving the k-Fibonacci and k-Jacobsthal numbers using define a new useful operator denoted by δbk1,b2
Summary
Introduction and PreliminariesFibonacci and Lucas numbers have been studied by many researchers for a long time to get intrinsic theory and applications of these numbers in many research areas as Physics, Engineering, Architecture, Nature and Art. In order to determine generating functions of the product of k-Fibonacci and k-Jacobsthal numbers and Chebychev polynomials of second kind, we combine between our indicated past techniques and these presented polishing approaches. B2n t n cases of the following Theorems. The new generating functions of the products of k-Fibonacci numbers, k-Pell numbers, k-Jacobsthal numbers and the Chebychev polynomials of the second kind are given by using the previous theorems.
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