DOI: 10.1515/dema-2025-0278 ISSN: 2391-4661

Series of convergence ratios “ ± 4 27 $\frac{{\pm}4}{27}$ ” containing harmonic numbers

Chunli Li, Wenchang Chu
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Abstract

Three accelerating transformation formulae for hypergeometric series are systematically analyzed by the “coefficient extraction method”. Numerous harmonic series of convergence ratios “

± 4 27 $\frac{{\pm}4}{27}$
” are evaluated in closed form, which fills a gap of series calculus since similar ones have not appeared often in the literature.

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