6 citations · 20 across the 39 of their papers we have counts for
42 papers
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…
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…
Double sums involving binomial coefficients and special numbers
Kunle Adegoke, Robert Frontczak, Karol Gryszka
In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving…
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…
Three combinatorial sums involving central binomial coefficients
Kunle Adegoke, Robert Frontczak
We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In…
Finite sums associated with some polynomial identities
Kunle Adegoke, Robert Frontczak, Karol Gryszka
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can…
Evaluation of harmonic number series involving the binomial coefficient in the denominator by integration
Kunle Adegoke, Robert Frontczak
Two classes of infinite series involving harmonic numbers and the binomial coefficient are evaluated in closed form using integrals. Several remarkable integral values an…
New harmonic number series
Kunle Adegoke, Robert Frontczak
Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inv…
Series associated with a forgotten identity of Nörlund
Kunle Adegoke, Robert Frontczak
We apply a seemingly forgotten series expression of Nörlund for the psi function to express infinite series involving inverse factorials in closed form. Many of such series contain…
Convolutions of second order sequences: A direct approach
Kunle Adegoke, Segun Olofin Akerele, Robert Frontczak
Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence rela…
Combinatorial identities with multiple harmonic-like numbers
Kunle Adegoke, Robert Frontczak
Multiple harmonic-like numbers are studied using the generating function approach. A closed form is stated for binomial sums involving these numbers and two additional parameters.…
Integration Formulas Involving Fibonacci and Lucas Numbers
Kunle Adegoke, Robert Frontczak
We present a range of difficult integration formulas involving Fibonacci and Lucas numbers and trigonometric functions. These formulas are often expressed in terms of special funct…
Some notes on an identity of Frisch
Kunle Adegoke, Robert Frontczak
In this note, we show how a combinatorial identity of Frisch can be applied to prove and generalize some well-known identities involving harmonic numbers. We also present some comb…
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…
General convolution sums involving Fibonacci m-step numbers
Robert Frontczak, Karol Gryszka
In this paper, using a generating function approach, we derive several new convolution sum identities involving Fibonacci m-step numbers. As special instances of the results derive…
Three new classes of binomial Fibonacci sums
Robert Frontczak
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients.
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 and divisibility properties
Kunle Adegoke, Robert Frontczak
Based on a variant of Sury's polynomial identity we derive new expressions for various finite Fibonacci (Lucas) sums. We extend the results to Fibonacci and Chebyshev polynomials,…