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