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The classical hypergeometric summation theorems are exploited to derive several striking identities on harmonic numbers including those discovered recently by Paule and Schneider (

By combining the linearization method with Dougall's sum for well-poised 5 F 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.

Trigonometric summations over the angles equally divided on the upper half plane are investigated systematically. Their generating functions are established by expansions of trigonometric polynomials in partial fractions. The explicit formulas are displayed and their proofs are presented in brief through the formal power series method.

Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented.

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By combining inverse series relations with binomial convolutions and telescoping method, moments of Catalan numbers are evaluated, which resolves a problem recently proposed by Gutiérrez et al. [J.M. Gutiérrez, M.A. Hernández, P.