Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theo...

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Published in:	Journal of inequalities and applications Vol. 2013; no. 1; pp. 1 - 11
Main Author:	Choi, Junesang
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.12.2013 Springer Nature B.V
Subjects:	Algorithms Analysis Applications of Mathematics Binomial coefficients Elementary particles Harmonics Inequalities Mathematical analysis Mathematics Mathematics and Statistics Operators Proceedings of the International Congress in Honour of Professor Hari M. Srivastava Series (mathematics) Stirling numbers of the first kind summation formulas for psi-function generalized hypergeometric function generalized harmonic numbers Riemann zeta function harmonic numbers polygamma functions Hurwitz zeta function
ISSN:	1029-242X, 1025-5834, 1029-242X
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Abstract	A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity. MSC: 11M06, 33B15, 33E20, 11M35, 11M41, 40C15.
AbstractList	A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity. MSC: 11M06, 33B15, 33E20, 11M35, 11M41, 40C15. A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity. MSC: 11M06, 33B15, 33E20, 11M35, 11M41, 40C15.[PUBLICATION ABSTRACT] A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity. MSC: 11M06, 33B15, 33E20, 11M35, 11M41, 40C15.
ArticleNumber	49
Author	Choi, Junesang
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Copyright	Choi; licensee Springer 2013. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Author(s) 2013
Copyright_xml	– notice: Choi; licensee Springer 2013. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. – notice: The Author(s) 2013
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Keywords	Stirling numbers of the first kind summation formulas for psi-function generalized hypergeometric function generalized harmonic numbers Riemann zeta function harmonic numbers polygamma functions Hurwitz zeta function
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SubjectTerms	Algorithms Analysis Applications of Mathematics Binomial coefficients Elementary particles Harmonics Inequalities Mathematical analysis Mathematics Mathematics and Statistics Operators Proceedings of the International Congress in Honour of Professor Hari M. Srivastava Series (mathematics)
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Title	Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers
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