6 citations · 20 across the 39 of their papers we have counts for
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On the Euler transform and the floor function
Robert Frontczak
Let be a sequence of numbers. We derive an expression for the Euler transform of a general binomial sum involving and weighted by the floor function. To dem…
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…
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 transfor…