Kunle Adegoke, Robert Frontczak, Taras Goy
Published 2024-01-04Version 1
We present several types of ordinary generating functions involving central binomial coefficients, harmonic numbers, and odd harmonic numbers. Our results complement those of Boyadzhiev from 2012 and Chen from 2016. Based on these generating functions we evaluate several infinite series in closed form. In addition, we offer some combinatorial sum identities involving Catalan numbers, harmonic numbers and odd harmonic numbers. Finally, we analyze a special log-integral with Fibonacci numbers and odd harmonic numbers.
Asymptotics of partial sums of central binomial coefficients and Catalan numbers
The freeness of Ish arrangements
Chebyshev polynomials, their remarkable properties and connection with Catalan numbers
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