Generalized hyperharmonic number sums with squared reciprocal binomial coefficients | Synapse
June 7, 2026Open Access
Generalized hyperharmonic number sums with squared reciprocal binomial coefficients
Key Points
This research aims to simplify generalized hyperharmonic number sums by expressing them in terms of classical sums.
Proved relationships between hyperharmonic number sums and classical Euler sums.
Analyzed connections with zeta values and harmonic numbers.
Demonstrated that hyperharmonic number sums can be expressed as combinations of classical sums.
Identified specific transformations involving alternating Euler sums and generalized harmonic numbers.
Abstract
In the current paper, we prove that the sums in the title can be reduced as combinations of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.