π-Formulae from dual series of the Dougall theorem
DOI:
https://doi.org/10.37863/umzh.v74i12.6587Keywords:
Classical hypergeometric series; The Dougall summation theorem; Gould-Hsu inverse series relations; Ramanujan's series for 1/π; Guillera's series for 1/π2.Abstract
UDC 517.5
By means of the extended Gould–Hsu inverse series relations, we find that the dual relation of Dougall's summation theorem for the well-poised 7F6-series can be used to construct numerous interesting Ramanujan-like infinite-series expressions for π±1 and π±2, including an elegant formula for π−2 due to Guillera.
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