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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…
On a problem of Mező and its generalizations to three classes of rational zeta series
Kunle Adegoke, Robert Frontczak, Taras Goy
We evaluate in closed form three special classes of alternating zeta series with one and two additional parameters. Two classes are expressed as linear combinations of polylogarith…