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http://dx.doi.org/10.5666/KMJ.2021.61.3.473

Lucas-Euler Relations Using Balancing and Lucas-Balancing Polynomials  

Frontczak, Robert (Landesbank Baden-Wurttemberg)
Goy, Taras (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.3, 2021 , pp. 473-486 More about this Journal
Abstract
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;
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