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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/1029-242X-2013-49