6 citations · 19 across the 34 of their papers we have counts for
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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*}…
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…
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…
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.…
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…