Remarkable series concerning $ \binom{3n}{n} $ and harmonic numbers in numerators-Reference-Cited by-同舟云学术

Remarkable series concerning $ \binom{3n}{n} $ and harmonic numbers in numerators

Published:2024 Issue:7 Volume:9 Page:17234-17258
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Li Chunli¹,Chu Wenchang²

Affiliation:

1. School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou (Henan), China

2. Via Dalmazio Birago 9/E, Lecce 73100, Italy

Abstract

<abstract><p>Three classes of infinite series containing binomial coefficient $ \binom{3n}{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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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