Double Sums Involving Binomial Coefficients and Special Numbers

Kunle Adegoke; Robert Frontczak; Karol Gryszka

doi:10.2478/amsil-2026-0013

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Double Sums Involving Binomial Coefficients and Special Numbers

Annales Mathematicae Silesianae

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By: Kunle Adegoke , Robert Frontczak and Karol Gryszka

Open Access

|Oct 2026

Abstract

In this paper, we find an elementary approach for double sums where the inner sum is binomial but incomplete. We apply our core identity and its relatives to double sums involving famous numbers such as harmonic numbers, Fibonacci numbers, Stirling numbers and r-Stirling numbers of the second kind.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2026-0013 | Journal eISSN: 2391-4238 (formerly 0860-2107) | Journal ISSN: 0860-2107

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Language: English

Submitted on: Jan 16, 2026

Accepted on: Sep 14, 2026

Published on: Oct 24, 2026

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

double sum,

binomial coefficient,

harmonic number,

Fibonacci number,

Stirling number

MSC:

05A10,

11B39,

11B65,

11B73

Related subjects:

Mathematics,

General mathematics

© 2026 Kunle Adegoke, Robert Frontczak, Karol Gryszka, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

AHEAD OF PRINT