  We calculate some finite and infinite sums containing the digamma function in
closed-form. For this purpose, we differentiate selected reduction formulas of
the hypergeometric function with respect to the parameters applying some
derivative formulas of the Pochhammer symbol. Also, we compare two different
differentiation formulas of the generalized hypergeometric function with
respect to the parameters. For some particular cases, we recover some results
found in the literature. Finally, all the results have been numerically
checked.
