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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…
A series of Ramanujan, two-term dilogarithm identities and some Lucas series
Kunle Adegoke, Robert Frontczak
We study an elementary series that can be considered a relative of a series studied by Ramanujan in Part 1 of his Lost Notebooks. We derive a closed form for this series in terms o…
Golden Ratio Base Expansions of the Logarithm and Inverse Tangent of Fibonacci and Lucas Numbers
Kunle Adegoke, Jaume Oliver Lafont
Let , the golden ratio, and . Let and be the Fibonacci and Lucas numbers, defined by and $L_n=α^n + β^…