What type of study is this?

This is a Quantitative Study study.

October 16, 2025Open Access

Three combinatorial sums involving central binomial coefficients

View Full Paper

Ask AI

Bookmark

The study develops recursive expressions for combinatorial sums involving central binomial coefficients and harmonic numbers.
Recursive expressions were derived using summation by parts for three classes of sums involving various harmonic numbers.
An alternative method was presented to show closed forms of certain sums in terms of Stirling numbers and r-Stirling numbers.
The implications of these findings enhance understanding of relationships between different classes of sums in combinatorial mathematics.

Implication

This research derives recursive expressions for combinatorial sums involving harmonic numbers, suggesting closed forms with Stirling numbers.

Abstract

We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive expressions for these sums. In addition, we offer an alternative approach to express one class of sums and some related sums in closed form in terms of Stirling numbers and r-Stirling numbers of the second kind.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Adegoke et al. (2025) studied this question.

synapsesocial.com/papers/68f147cc724575985c3fd0f4 https://doi.org/10.48550/arxiv.2505.09636

View Full Paper

Ask AI

Bookmark

Implication

This research derives recursive expressions for combinatorial sums involving harmonic numbers, suggesting closed forms with Stirling numbers.

Three combinatorial sums involving central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

Three combinatorial sums involving central binomial coefficients

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading