Gauss’ Second Theorem for F12(1/2)-Series and Novel Harmonic Series Identities-Reference-Cited by-同舟云学术

Gauss’ Second Theorem for F12(1/2)-Series and Novel Harmonic Series Identities

Published:2024-05-01 Issue:9 Volume:12 Page:1381
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Li Chunli¹^ORCID,Chu Wenchang²^ORCID

Affiliation:

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

2. Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy

Abstract

Two summation theorems concerning the F12(1/2)-series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in closed form, including eight conjectured ones made by Z.-W. Sun. The presented comprehensive coverage for the harmonic series of convergence rate “1/2” may serve as a reference source for readers.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/9/1381/pdf

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