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Abstract
We establish some identities of Euler related sums. By using these identities, we discuss the closed form representations of sums of harmonic numbers and reciprocal parametric binomial coefficients through parametric harmonic numbers, shifted harmonic numbers and Riemann zeta function with positive integer arguments. In particular, we investigate products of quadratic and cubic harmonic numbers and reciprocal parametric binomial coefficients. Some illustrative special cases as well as immediate consequences of the main results are also considered.
Acknowledgments
All authors thank the anonymous referee for many invaluable comments and suggestions which have improved the paper greatly.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
Ce Xu is supported by the National Natural Science Foundation of China [grant number 12101008], the Natural Science Foundation of Anhui Province [grant number 2108085QA01] and the University Natural Science Research Project of Anhui Province [grant number KJ2020A0057].