13 papers
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…
A combinatorial sum with two complex parameters
Michel Bataille, Robert Frontczak
This article deals with combinatorial identities with two complex parameters. Starting with a fundamental lemma, we derive various polynomial identities, combinatorial sums and rel…
Combinatorial sums derived from properties of Legendre polynomials
Michel Bataille, Robert Frontczak
From an identity connecting a combinatorial sum and Legendre polynomials, we derive closed forms for a number of combinatorial sums. Some of them are obtained via results about the…
New sums mixing harmonic numbers and central binomial coefficients
Micheal Bataille, Robert Frontczak
We study two new classes of sums with inverse binomial coefficients and harmonic numbers. In addition we establish recursive solutions to the following power sums \begin{equation*}…
Applications of an identity of Batır
Kunle Adegoke, Robert Frontczak
Based on an interesting identity of Batır we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transfo…
Double sums associated with binomial transforms
Kunle Adegoke, Robert Frontczak, Karol Gryszka
In this paper, we continue our investigation of double sums where the inner sum is binomial but incomplete. We prove many new results for these types of double sums associated with…