6 citations · 20 across the 39 of their papers we have counts for
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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…