  Following the Mellin and inverse Mellin transform techniques presented in our
paper arXiv:1606.02150 (NT), we have established close forms of Laurent series
expansions of products of bi- and trigamma functions /psi(z)*/psi(-z) and
/psi_(1)(z)*/psi_(1)(-z). These series were used to find summation rules which
include generalized harmonic numbers of first, second and third powers and
values of the Riemann zeta-functions at integers / Bernoulli numbers, for
example 2*Sum_(k-1)^(infinity)(H_(k)^((2))/k^3)=6*/zeta(2)*/zeta(3)-9*/zeta(5).
Some of these rules were tested numerically.
