6 citations · 18 across the 20 of their papers we have counts for
22 papers
Harmonic Catalan Number Series via Half-Integer Binomial Coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop a method for evaluating finite and infinite series involving Catalan numbers by specializing alternating binomial identities at half-integer parameters. The key ingredie…
Abel-Type Transformations and Telescoping Structures in Reciprocal Series of Second-Order Linear Recurrences
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop a unified method for transforming and evaluating infinite series involving products of terms of second-order linear recurrences in the denominator. The approach is based…
On Some Series Involving the Central Binomial Coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
In this paper, we explore a variety of series involving the central binomial coefficients, highlighting their structural properties and connections to other mathematical objects. S…
Evaluation of some alternating series involving the binomial coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
We evaluate in closed form several alternating infinite series involving the binomial coefficients and in the denominator. One of our results generalizes…
Combinatorial sums, series and integrals involving odd harmonic numbers
Kunle Adegoke, Robert Frontczak, Taras Goy
We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyad…
Fibonacci sums modulo 5
Kunle Adegoke, Robert Frontczak, Taras Goy
We develop closed form expressions for various finite binomial Fibonacci and Lucas sums depending on the modulo 5 nature of the upper summation limit. Our expressions are inferred…
Binomial sum relations involving Fibonacci and Lucas numbers
Kunle Adegoke, Robert Frontczak, Taras Goy
In this paper, we introduce relations between binomial sums involving (generalized) Fibonacci and Lucas numbers, and different kinds of binomial coefficients. We also present some…
Binomial Fibonacci sums from Chebyshev polynomials
Kunle Adegoke, Robert Frontczak, Taras Goy
We explore new types of binomial sums with Fibonacci and Lucas numbers. The binomial coefficients under consideration are and $\frac{k}{n+k}\binom{n…
On some series involving the binomial coefficients
Kunle Adegoke, Robert Frontczak, Taras Goy
Using a simple transformation, we obtain much simpler forms for some series involving binomial coefficients derived by Necdet Batir. New evaluations are given; and co…
Series and sums involving the floor function
Kunle Adegoke, Robert Frontczak, Taras Goy
Let be an arbitrary sequence and its dual floor sequence. We study infinite series and finite generalized binomial sums invo…
Some notes on a Fibonacci-Lucas identity
Kunle Adegoke, Robert Frontczak, Taras Goy
In 2016, Edgar and, independently of him, Bhatnagar sta\-ted a nice polynomial identity that connects Fibonacci and Lucas numbers. Shortly after their publications, this identity h…
The integrals in Gradshteyn and Ryzhik. Part 1: An Addendum
Kunle Adegoke, Robert Frontczak, Taras Goy
We present another generalization of a logarithmic integral studied by V.~H. Moll in 2007. The family of integrals contains three free parameter and its evaluation involves the har…
New binomial Fibonacci sums
Kunle Adegoke, Robert Frontczak, Taras Goy
We present some new linear, quadratic, cubic and quartic binomial Fibonacci, Lucas and Fibonacci--Lucas summation identities.
Additional Fibonacci-Bernoulli relations
Kunle Adegoke, Robert Frontczak, Taras Goy
We continue our study on relationships between Fibonacci (Lucas) numbers and Bernoulli numbers and polynomials. The derivations of our results are based on functional equations for…
Fibonacci-Catalan Series
Kunle Adegoke, Robert Frontczak, Taras Goy
We study certain series with Catalan numbers and reciprocal Catalan numbers, respectively, and provide seemingly new closed form evaluations of these series with Fibonacci (Lucas)…
On a family of infinite series with reciprocal Catalan numbers
Kunle Adegoke, Robert Frontczak, Taras Goy
We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Cata…
Reciprocal series involving Horadam numbers
Kunle Adegoke, Robert Frontczak, Taras Goy
We evaluate some new three parameter families of finite reciprocal sums involving Horadam numbers. We will also be able to state the results for the infinite sums. Some Fibonacci a…
Chebyshev-Fibonacci polynomial relations using generating functions
Robert Frontczak, Taras Goy
The main object of the paper is to reveal connections between Chebyshev polynomials of the first and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved…
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.