On some conjectural series containing harmonic numbers of 3-order

2023/08/12 by Wei, Chuanan, Xu, Ce
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.06440

Abstract

Harmonic numbers are important in a lot of branches of number theory. By means of the derivative operator, the integral operator, and several summation and transformation formulas for hypergeometric series, we prove four series containing harmonic numbers of 3-order. Three of them are conjectures which were recently proposed by Z.-W. Sun.

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