On some conjectural series containing harmonic numbers of 3-order

Published 12 Aug 2023 in math.CO | (2308.06440v1)

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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