Computation and theory of Mordell–Tornheim–Witten sums II

In Bailey et al. [8] the current authors, along with the late and much-missed Richard Crandall (1947–2012), considered generalized Mordell–Tornheim–Witten (MTW) zeta-function values along with their derivatives, and explored connections with multiple-zeta values (MZVs). This entailed use of symbolic integration, high precision numerical integration, and some interesting combinatorics and special-function theory. The original motivation was to represent objects such as Eulerian log-gamma integrals; and all such integrals were expressed in terms of a MTW basis. Herein, we extend the research envisaged in Bailey et al. [8] by analyzing the relations between a significantly more general class of MTW sums. This has required significantly more subtle scientific computation and concomitant special function theory.