On some combinatorial identities and harmonic sums-Reference-Cited by-同舟云学术

On some combinatorial identities and harmonic sums

Published:2017-02 Issue:07 Volume:13 Page:1695-1709
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Batir Necdet¹

Affiliation:

1. Department of Mathematics, Nevşehir HBV University, Nevşehir, 50300, Turkey

Abstract

For any [Formula: see text] we first give new proofs for the following well-known combinatorial identities [Formula: see text] and [Formula: see text] and then we produce the generating function and an integral representation for [Formula: see text]. Using them we evaluate many interesting finite and infinite harmonic sums in closed form. For example, we show that [Formula: see text] and [Formula: see text] where [Formula: see text] are generalized harmonic numbers defined below.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179304211750097X

Reference36 articles.

1. On Stirling numbers and Euler sums

2. Problems: 10487-10493

3. Ramanujan’s Notebooks

Cited by 16 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Symmetric functions and a natural framework for combinatorial and number theoretic sequences;Research in Number Theory;2023-07-09

2. Sums involving the binomial coefficients, Bernoulli numbers of the second kind and harmonic numbers;Notes on Number Theory and Discrete Mathematics;2023-02-27

3. A New Proof of Boole’S Additive Combinatorics Formula;Discrete Mathematics Letters;2022-09-02

4. Log-hyperbolic tangent integrals and Euler sums;Advanced Studies: Euro-Tbilisi Mathematical Journal;2022-06-01

5. On Multisets, Interpolated Multiple Zeta Values and Limit Laws;The Electronic Journal of Combinatorics;2022-03-11