Other functions defined by series and integrals (msc 33E20), Other Dirichlet series and zeta functions (msc 11M41), Gamma, beta and polygamma functions (msc 33B15), Other functions coming from differential, difference and integral equations (msc 33E30), Difference equations, additive (msc 39A10)
Academic Press
Advances in Mathematics

Ruijsenaars, S.N.M. (2000). On Barnes' multiple zeta and gamma functions. Advances in Mathematics, 156(1), 107–132.