In this paper we generalize to bivariate Fibonacci and Lucas polynomials, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate bases are families of integers satisfying remarkable recurrence relations.
This paper is devoted to the study of certain unimodal sequences related to binomial coefficients. Although the paramount purpose is to prove unimodality, in a few cases we even determine the maxima of the sequences. Our new results generalize some earlier theorems on unimodality. The proof techniques are quite varied.
Letting T n (resp. U n) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences X k T n−k k and X k U n−k k for n − 2 n/2 ≤ k ≤ n − n/2 are two basis of the Q-vectorial space E n [X] formed by the polynomials of Q [X] having the same parity as n and of degree ≤ n. Also T n and U n admit remarkableness integer… (More)
In this paper, we establish several formulae for sums and alternating sums of products of generalized Fibonacci and Lucas numbers. In particular, we recover and extend all results of Z.
Quality Function Deployment (QFD) is an effective tool to enhance customer satisfaction, develop the product quality and enhance competitive advantages in the market. In developing new products and projects, we receive the needs from the customer, pass it around a corporate communication circle, and eventually return it to the customer in the form of the… (More)
In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.