Let $ (T_{n})_{n\ge 0} $ be the sequence of Tribonacci numbers defined by $ T_0=0 $, $ T_1=T_2=1$, and $ T_{n+3}= T_{n+2}+T_{n+1} +T_n$ for all $ n\ge 0 $. In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two repdigits.

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Tribonacci numbers that are concatenations of two repdigits.

In this paper, we introduce an operator in order to derive some new symmetric properties of -Lucas numbers and Lucas polynomials. By making use of the operator defined in this paper, we give some new generating functions for -Lucas numbers and Lucas polynomials.

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On the k -Lucas Numbers and Lucas Polynomials

In this paper we show how the action of the symmetrizing endomorphism operator � k e1e2 to the series 1 P j=0 a je j 1z j allows us to obtain an alternative approach for the determination of some generalized sequence of numbers.

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A simple and accurate method for determination of some generalized sequence of numbers

Abstract: In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss Lucas polynomials, bivariate Fibonacci polynomials, bivariate Lucas polynomials, bivariate Jacobsthal polynomials and bivariate Jacobsthal Lucas polynomials.

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Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials

In this paper, a novel normalized Lucas wavelet scheme based on tau approach is proposed for the two classes of second-order differential equations, namely Lane–Emden and pantograph equations. The introduced scheme depends on shifted Lucas polynomials (SLPs) and their operational matrix of derivative (which are developed here). The weight function for the orthogonality of Lucas polynomials, and Rodrigues formula are proposed for the first time, which form the basis for the construction of SLPs. Normalized Lucas wavelets are constructed by utilizing SLPs and their novel properties. Literally, the present scheme transforms the given method to a set of nonlinear algebraic equations with undetermined coefficients which are here tackled by tau method. Meanwhile, new treatment of convergence and error analysis is provided for the established approach. Finally, the accuracy and applicability of present scheme is ensured by considering several examples.

Normalized Lucas wavelets: an application to Lane–Emden and pantograph differential equations

In this paper, we calculate the generating functions by using the con- cepts of symmetric functions. Although the methods cited in previous works are in principle constructive, we are concerned here only with the question of manipulating combinatorial objects, known as symmetric op- erators. The proposed generalized symmetric functions can be used to find explicit formulas of the Fibonacci numbers, and of the Tchebychev polynomials of first and second kinds.

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Symmetric and generating functions

In this paper, we propose an alternative approach for the determination of the Fibonacci numbers and some results of Foata, Ramanujan and other results on Tchebychev polynomials of the first and second kinds. This approach is based on the action of the symmetrizing operator Le1e2 on the series P1 j=0 ajz j . Obtained results confirm the e↵ectiveness of the proposed approach. 1. Preliminaries and Notation Here, we recall some basic definitions and theorems that are needed in the sequel. Given two sets of indeterminates A and B (called alphabets), we define a symmetric function Sj(A B) as in [1]: ⇧b2B(1 zb) ⇧a2A(1 za) = 1 X

Ali Boussayoud

Papers

Symmetric and generating functions

On the k -Lucas Numbers and Lucas Polynomials

Some Applications of Symmetric Functions.

A simple and accurate method for determination of some generalized sequence of numbers

Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials