Harmonic Series of Convergence Ratio “1/4" with Cubic Central Binomial Coefficients

We examine a useful hypergeometric transformation formula by means of the coefficient extraction method. A large class of “binomial/harmonic series” (of convergence ratio “1/4”) containing the cubic central binomial coefficients and harmonic numbers is systematically investigated. Numerous closed summation formulae are established, including a remarkable series about harmonic numbers of the third order.