ON GUILLERA'S F-7(6)((64)/(27))-SERIES FOR 1/p(2)

In 2011, Guillera ["A new Ramanujan-like series for 1/pi(2)', Ramanujan J. 26 (2011), 369-374] introduced a remarkable rational F-7(6)( (64)/(27))-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 F-5(4)-sum. Another proof of Guillera's F-7(6)( (64)/(27))-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 F-7(6)( (64)/(27))-series. The many past research articles concerning Guillera's F-7(6)( (64)/(27))-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 F-7(6)( (64)/(27))-and F-6(5)( (64)/(27))-series for root 2.