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- W4319764868 abstract "Abstract In 2011, Guillera [‘A new Ramanujan-like series for $1/pi ^2$ ’, Ramanujan J. 26 (2011), 369–374] introduced a remarkable rational ${}_{7}F_{6}( frac {27}{64} )$ -series for ${1}/{pi ^2}$ using the Wilf–Zeilberger (WZ) method, and Chu and Zhang later proved this evaluation using an acceleration method based on Dougall’s ${}_{5}F_{4}$ -sum. Another proof of Guillera’s ${}_{7}F_{6}( frac {27}{64} )$ -series was given by Guillera in 2018, and this subsequent proof used a recursive argument involving Dougall’s sum together with the WZ method. Subsequently, Chen and Chu introduced a q -analogue of Guillera’s ${}_{7}F_{6}( frac {27}{64} )$ -series. The many past research articles concerning Guillera’s ${}_{7}F_{6}( frac {27}{64} )$ -series for ${1}/{pi ^2}$ naturally lead to questions about similar results for other mathematical constants. We apply a WZ-based acceleration method to prove new rational ${}_{7}F_{6}( frac {27}{64} )$ - and ${}_{6}F_{5}( frac {27}{64} )$ -series for $sqrt {2}$ ." @default.
- W4319764868 created "2023-02-11" @default.
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- W4319764868 date "2023-02-09" @default.
- W4319764868 modified "2023-09-28" @default.
- W4319764868 title "ON GUILLERA’S -SERIES FOR" @default.
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- W4319764868 doi "https://doi.org/10.1017/s0004972723000060" @default.
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