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Research Article | Open Access

Remarkable series concerning ( 3 n n ) and harmonic numbers in numerators

Chunli Li1, Wenchang Chu2( )
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), China
Via Dalmazio Birago 9/E, Lecce 73100, Italy
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Abstract

Three classes of infinite series containing binomial coefficient ( 3 n n ) , harmonic-like numbers, and an independent variable " y" are examined. Several algebraic formulae in closed form are established, including, as special cases, three conjectured values for numerical series by Z.-W. Sun. This is fulfilled by integrating Lambert's series and manipulating the cubic transformations for the 3 F 2 -series through the "coefficient extraction" method.

Keywords

Lambert's seriesharmonic numberbinomial coefficientdilogarithm functionBailey's cubic transformation
CLC number: Primary 11B65; Secondary 33C20, 65B10

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 17234-17258
DOI: 10.3934/math.2024837

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Cite this article:
Li C, Chu W. Remarkable series concerning ( 3 n n ) and harmonic numbers in numerators. AIMS Mathematics, 2024, 9(7): 17234-17258. https://doi.org/10.3934/math.2024837

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Received: 26 March 2024
Revised: 11 May 2024
Accepted: 15 May 2024
Published: 15 July 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)