Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.

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Bibliographic Details
Published in:Journal of difference equations and applications Vol. 23; no. 7; pp. 1204 - 1218
Main Authors: Liu, Hongmei, Zhou, Wenshu, Ding, Shuyan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03.07.2017
Taylor & Francis Ltd
Subjects:
33C20
Applied mathematics
derivative
digamma functions
Harmonic number summation formulae
Hypergeometric series
Numbers
Theorems
ISSN:1023-6198, 1563-5120
Online Access:Get full text
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Description
Summary:By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.
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ISSN:1023-6198
1563-5120
DOI:10.1080/10236198.2017.1318861