Series of Convergence Rate −1/4 Containing Harmonic Numbers-Reference-Cited by-同舟云学术

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Series of Convergence Rate −1/4 Containing Harmonic Numbers

Published:2023-05-24 Issue:6 Volume:12 Page:513
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Li Chunli¹^ORCID,Chu Wenchang¹^ORCID

Affiliation:

1. School of Mathematics and Statistics, Zhoukou Normal University, Zhuokou 466001, China

Abstract

Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients. Among them, three conjectured identities due to Z.-W. Sun are also confirmed.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/6/513/pdf

Reference20 articles.

1. Rainville, E.D. (1960). Special Functions, The Macmillan Company.

2. Hypergeometric series and the Riemann Zeta function;Chu;Acta Arith.,1997

3. Alternating series of Apéry–type series for the Riemann zeta function;Chu;Contrib. Discrete Math.,2020

4. Comtet, L. (1974). Advanced Combinatorics, Dordrecht–Holland.

5. Series with central binomial coefficients, Catalan numbers, and harmonic numbers;Boyadzhiev;J. Integer Seq.,2012

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