Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Generalized Tribonacci Polynomials
View through CrossRef
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.
Title: Generalized Tribonacci Polynomials
Description:
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.
Related Results
Truncated-Exponential-Based Appell-Type Changhee Polynomials
Truncated-Exponential-Based Appell-Type Changhee Polynomials
The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known pol...
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
Generating Functions for New Families of Combinatorial Numbers and Polynomials: Approach to Poisson–Charlier Polynomials and Probability Distribution Function
The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and ...
On λ-Changhee–Hermite polynomials
On λ-Changhee–Hermite polynomials
Abstract
In this paper, we introduce a new class of
λ-analogues of the Changhee–Hermite polynomials and
generalized Gould–Hopper–Appell type λ-Changhee polynomials,
...
Krein–Sobolev Orthogonal Polynomials II
Krein–Sobolev Orthogonal Polynomials II
In a recent paper, Littlejohn and Quintero studied the orthogonal polynomials {Kn}n=0∞—which they named Krein–Sobolev polynomials—that are orthogonal in the classical Sobolev space...
Novel/Old Generalized Multiplicative Zagreb Indices of Some Special Graphs
Novel/Old Generalized Multiplicative Zagreb Indices of Some Special Graphs
Topological descriptor is a fixed real number directly attached with the molecular graph to predict the physical and chemical properties of the chemical compound. Gutman and Trinaj...
On square Tribonacci Lucas numbers
On square Tribonacci Lucas numbers
The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 1...
Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials
Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials
Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials...
Mittag-Leffler-Gould-Hopper polynomials: Symbolic Approach
Mittag-Leffler-Gould-Hopper polynomials: Symbolic Approach
The paper describes the method of symbolic evaluation that serves as a
useful tool to extend the studies of certain special functions including
their properties and capabilities. I...