$\pi$-Formulae from dual series of the Dougall theorem

W.  Chu

doi:10.37863/umzh.v74i12.6587

W. Chu School Math. and Statistics, Zhoukou Normal Univ., Henan, China and Univ. Salento, Italy

DOI: https://doi.org/10.37863/umzh.v74i12.6587

Анотація

УДК 517.5

$\pi$-формули з дуальних рядів теореми Дугалла

За допомогою узагальнених співвідношень Гулда та Хсу для оберненого ряду доведено, що дуальне співвідношення теореми підсумовування Дугалла для добре збалансованого $_7F_6$-ряду можна використати для побудови багатьох цікавих виразів для нескінченного ряду, подібних до виразів, що були отримані Рамануджаном для $\pi^{\pm1}$ і $\pi^{\pm2},$ включаючи елегантну формулу Гільєра для $\pi^{-2}$.

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