π-Formulae from dual series of the Dougall theorem
DOI:
https://doi.org/10.37863/umzh.v74i12.6587Ключові слова:
Classical hypergeometric series; The Dougall summation theorem; Gould-Hsu inverse series relations; Ramanujan's series for 1/π; Guillera's series for 1/π2.Анотація
УДК 517.5
π-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 7F6-ряду можна використати для побудови багатьох цікавих виразів для нескінченного ряду, подібних до виразів, що були отримані Рамануджаном для π±1 і π±2, включаючи елегантну формулу Гільєра для π−2.
Посилання
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