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

Chunli Li and Wenchang Chu ()
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Chunli Li: School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
Wenchang Chu: Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy

Mathematics, 2024, vol. 12, issue 9, 1-12

Abstract: Two summation theorems concerning the F 1 2 ( 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.

Keywords: harmonic number; gamma function; binomial/multinomial coefficient (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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