Weighted sums of squares via generalized eulerian polynomials

Pita-Ruiz, Claudio

Weighted sums of squares via generalized eulerian polynomials

Journal

Fibonacci Quarterly

ISSN

0015-0517

Date Issued

2017

Author(s)

Pita-Ruiz, Claudio

Facultad de Ingeniería - CampCM

Type

text::conference output::conference proceedings::conference paper

URL

https://scripta.up.edu.mx/handle/20.500.12552/4795

https://www.fq.math.ca/Papers1/55-5/Stanica.pdf

Abstract

We give explicit formulas for the weighted sum of squares σm-1 j=0 zj (aj + b)2, where a, b ∈ C are given, and z ∈ C, z ≠ 0, 1 is the weight. In the case a, b ∈ Z and z ∈ Q, we show that there is a one-To-one correspondence between our weighted sums and Primitive Pythagorean Triples. The main tools we use are the Z-Transform of sequences and a generalization of Eulerian polynomials. Copyright © 2017 The Fibonacci Association. All rights reserved.

How to cite

Pita Ruiz Velasco, C. J. (2017). Weighted sums of squares via generalized eulerian polynomials. Fibonacci Quarterly, 55 (5) 149-165 i