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

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

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 $\pi^{-2}$.

Посилання

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Опубліковано
17.01.2023
Як цитувати
ChuW. «$\pi$-Formulae from Dual Series of the Dougall Theorem». Український математичний журнал, вип. 74, вип. 12, Січень 2023, с. 1686 -08, doi:10.37863/umzh.v74i12.6587.
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