Generalized Tribonacci Polynomials

Abstract

In this paper, we investigate the generalized Tribonacci polynomials and we deal with, in detail, two special cases which we call them (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials. We also introduce and investigate a new sequence and its two special cases namely the generalized co-Tribonacci, (r,s,t)-co-Tribonacci and (r,s,t)-co-Tribonacci-Lucas polynomials, respectively. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these polynomial sequences. Moreover, we give some identities and matrices related to these polynomials. Furthermore, we evaluate the infinite sums of special cases of (r,s,t)-Tribonacci and (r,s,t)-Tribonacci-Lucas polynomials.