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Accelerating the convergence of some hypergeometric series with Gosper's method leads, in a most elementary way, to some series discovered by Ramanujan, Bauer and Dougall. In particular, it is shown that one of them can be traced back to the well-known formula of Wallis.
Anthony Christopher Davison, Soumaya Elkantassi
Victor Panaretos, Neda Mohammadi Jouzdani