Certain summation formulas involving harmonic numbers and generalized harmonic numbers

Harmonic numbers and generalized harmonic numbers have been studied 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 aim at present...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 218; no. 3; pp. 734 - 740
Main Author: Choi, Junesang
Format: Journal Article
Language:English
Published: Elsevier Inc 01.10.2011
Subjects:
Algorithms
Elementary particles
Generalized harmonic numbers
Generalized hypergeometric function pFq
Harmonic numbers
Harmonics
Hurwitz Zeta function
Hypergeometric functions
Infinite series
Mathematical analysis
Mathematical models
Number theory
Polygamma functions
Psi-function
Riemann Zeta function
Stirling numbers of the first kind
Summation formulas for pFq
Stirling numbers of the first kind
Harmonic numbers
Generalized hypergeometric function p F q
Polygamma functions
Generalized harmonic numbers
Psi-function
Riemann Zeta function
Summation formulas for p F q
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Harmonic numbers and generalized harmonic numbers have been studied 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 aim at presenting further interesting identities about certain finite or infinite series involving harmonic numbers and generalized harmonic numbers by applying an algorithmic method to a known summation formula for the hypergeometric function 5 F 4(1).
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.01.062