What does this research mean for the field?

Recursive solutions can be established for specific power sums involving inverse central binomial coefficients and harmonic numbers, alongside the introduction of two new classes of such sums. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish recursive solutions and evaluation methods for new classes of power sums combining inverse central binomial coefficients and harmonic numbers.

September 5, 2026The Fibonacci quarterlyOpen Access

New sums mixing harmonic numbers and central binomial coefficients

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To establish recursive solutions and evaluation methods for new classes of power sums combining inverse central binomial coefficients and harmonic numbers.
Analyzed algebraic series involving reciprocal central binomial coefficients weighted by polynomial powers.
Formulated recurrence relations for power sums Ud(n) and harmonic-weighted sums Vd(n) across positive integer exponents d.
Derived explicit recursive solutions to compute power sums Ud(n) involving reciprocal central binomial coefficients for arbitrary positive integers d.
Established recurrence relations for harmonic-weighted series Vd(n), enabling closed evaluations without term-by-term summation.

Implication

Mathematical study derives recursive solutions for power sums containing harmonic numbers and central binomial coefficients, suggesting simpler evaluations of inverse series.

Abstract

We study two new classes of sums with inverse binomial coefficients and harmonic numbers. In addition we establish recursive solutions to the following power sums {equation*} U_d(n) = ∑ₖ₌₁^n {2²ᵏ}{{2k}{k}} · k^d and V_d(n) = ∑ₖ₌₁^n {2²ᵏ}{{2k}{k}}· k^d\,H_k, {equation*} where d is a positive integer.

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Cite This Study

Bataille et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd3726b95aff0620eab1f https://doi.org/10.1080/00150517.2026.2706509

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Implication

Mathematical study derives recursive solutions for power sums containing harmonic numbers and central binomial coefficients, suggesting simpler evaluations of inverse series.

New sums mixing harmonic numbers and central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

New sums mixing harmonic numbers and central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

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