By combining the linearization method with Dougall’s sum for well–poised $_5F_4$ -series, we investigate the generalized Watson series with two extra integer parameters. Four analytical formulae are established, which can also be used to evaluate the extended Whipple and Dixon series via the Thomae transformation. Twelve concrete formulae are presented as exemplification.

The modified Abel lemma on summation by parts is employed to investigate the partial sum of Dougall’s $_5H_5$ -series. Several unusual transformation formulae into fast convergent series are established. They lead surprisingly to numerous infinite series identities involving $\pi$ , $\zeta (3)$ and the Catalan constant, including several important ones discovered by Ramanujan (1914) and recently by Guillera.

The modified Abel lemma on summation by parts is employed to investigate the partial sum of Dougall’s bilateral $_2H_2$ -series. Several unusual transformations into fast convergent series are established. They lead surprisingly to numerous infinite series expressions for $\pi$ , including several formulae discovered by Ramanujan (1914) and recently by Guillera (2008).

By means of series–rearrangements and finite differences, elementary proofs are presented for the well–known convolution identities of Abel and Hagen–Rothe.