Two problems of binomial sums involving harmonic numbers

Abstract Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric functions.

Bibliographic Details
Main Authors:	Nadia N. Li, Wenchang Chu
Format:	Article
Language:	English
Published:	SpringerOpen 2021-04-01
Series:	Advances in Difference Equations
Subjects:	Binomial coefficient Harmonic number Signless Stirling number Symmetric function Partial fraction decomposition
Online Access:	https://doi.org/10.1186/s13662-021-03383-z

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spelling	doaj-6a908fbdbaba48668540fd328291b6452021-05-02T11:43:01ZengSpringerOpenAdvances in Difference Equations1687-18472021-04-012021111010.1186/s13662-021-03383-zTwo problems of binomial sums involving harmonic numbersNadia N. Li0Wenchang Chu1School of Mathematics and Statistics, Zhoukou Normal UniversitySchool of Mathematics and Statistics, Zhoukou Normal UniversityAbstract Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric functions.https://doi.org/10.1186/s13662-021-03383-zBinomial coefficientHarmonic numberSignless Stirling numberSymmetric functionPartial fraction decomposition
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nadia N. Li Wenchang Chu
spellingShingle	Nadia N. Li Wenchang Chu Two problems of binomial sums involving harmonic numbers Advances in Difference Equations Binomial coefficient Harmonic number Signless Stirling number Symmetric function Partial fraction decomposition
author_facet	Nadia N. Li Wenchang Chu
author_sort	Nadia N. Li
title	Two problems of binomial sums involving harmonic numbers
title_short	Two problems of binomial sums involving harmonic numbers
title_full	Two problems of binomial sums involving harmonic numbers
title_fullStr	Two problems of binomial sums involving harmonic numbers
title_full_unstemmed	Two problems of binomial sums involving harmonic numbers
title_sort	two problems of binomial sums involving harmonic numbers
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2021-04-01
description	Abstract Two open problems recently proposed by Xi and Luo (Adv. Differ. Equ. 2021:38, 2021) are resolved by evaluating explicitly three binomial sums involving harmonic numbers, that are realized mainly by utilizing the generating function method and symmetric functions.
topic	Binomial coefficient Harmonic number Signless Stirling number Symmetric function Partial fraction decomposition
url	https://doi.org/10.1186/s13662-021-03383-z
work_keys_str_mv	AT nadianli twoproblemsofbinomialsumsinvolvingharmonicnumbers AT wenchangchu twoproblemsofbinomialsumsinvolvingharmonicnumbers
_version_	1721491849765453824

Two problems of binomial sums involving harmonic numbers

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