Derivative operator and harmonic number identities
Chuanan Wei, Dianxuan Gong
TL;DR
This paper derives a general harmonic number identity using derivative operators on hypergeometric series, leading to new Chu-Donno and Paule-Schneider type identities.
Contribution
It introduces a novel method applying derivative operators to hypergeometric series to generate broad harmonic number identities.
Findings
Established a general harmonic number identity.
Derived several Chu-Donno type identities.
Produced Paule-Schneider type identities.
Abstract
By applying the derivative operator to the corresponding hypergeometric form of a -series transformation due to Andrews [1,Theorem 4], we establish a general harmonic number identity. As the special cases of it, several interesting Chu-Donno type identities and Paule-Schneider type identities are displayed.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities