Article
Kyungpook Mathematical Journal 2021; 61(3): 473-486
Published online September 30, 2021
Copyright © Kyungpook Mathematical Journal.
Lucas-Euler Relations Using Balancing and Lucas-Balancing Polynomials
Robert Frontczak, Taras Goy*
Landesbank Baden-Württemberg, Stuttgart 70173, Germany
e-mail : robert.frontczak@lbbw.de
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk 76018, Ukraine
e-mail : taras.goy@pnu.edu.ua
Received: October 21, 2021; Revised: March 12, 2021; Accepted: March 23, 2021
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on functional equations for the respective generating functions. From these polynomial relations, we deduce interesting identities with Fibonacci and Lucas numbers, and Euler numbers. The results must be regarded as companion results to some Fibonacci-Bernoulli identities, which we derived in our previous paper.
Keywords: Euler polynomials and numbers, Bernoulli numbers, balancing polynomials and numbers, Fibonacci numbers, generating function.