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Lucas-Euler relations using balancing and Lucas-balancing polynomials
Robert Frontczak, Taras Goy
We establish some new combinatorial identities involving Euler polynomials and balancing (Lucas-balancing) polynomials. The derivations use elementary techniques and are based on f…
More Fibonacci-Bernoulli relations with and without balancing polynomials
Robert Frontczak, Taras Goy
We continue our study on relationships between Bernoulli polynomials and balancing (Lucas-balancing) polynomials. From these polynomial relations, we deduce new combinatorial ident…
Additional close links between balancing and Lucas-balancing polynomials
Robert Frontczak, Taras Goy
Using generating functions, we derive many identities involving balancing and Lucas-balancing polynomials. By relating these polynomials to Chebyshev polynomials of the first and s…
General infinite series evaluations involving Fibonacci numbers and the Riemann Zeta function
Robert Frontczak, Taras Goy
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.