For further sums involving the psi function see
Hansen (1975, pp. 360–367). For sums of gamma functions see
Andrews et al. (1999, Chapters 2 and 3) and §§15.2(i),
For related sums involving finite field analogs of the gamma and beta functions
(Gauss and Jacobi sums) see Andrews et al. (1999, Chapter 1) and
Terras (1999, pp. 90, 149).