π-Formulas from Dual Series of the Dougall Theorem

π-Formulas from Dual Series of the Dougall Theorem

By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised 7 F 6 -series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π ± 1 and π ± 2 , including an elegant formula for π...

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Veröffentlicht in:Ukrainian mathematical journal 2023-05, Vol.74 (12), p.1924-1949
1. Verfasser: Chu, W.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Formulas (mathematics)
Geometry
Mathematics
Mathematics and Statistics
Statistics
Theorems
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Zusammenfassung:By means of the extended Gould–Hsu inverse series relations, we show that the dual relation of Dougall’s summation theorem for a well-poised 7 F 6 -series can be used to construct numerous interesting Ramanujanlike infinite-series expressions for π ± 1 and π ± 2 , including an elegant formula for π − 2 due to Guillera.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-023-02179-6