Evaluation of multiple zeta values for various limiting processes at non-positive integers

Multiple zeta values at non-positive integers depend on its limiting process. In this paper, explicit and recurrence formulas to evaluate multiple zeta values at non-positive integers for various limiting processes are given. As applications of them, a classification of multiple zeta values for ordered limits and relationship between multiple zeta values for directional limits and ordered limits are showed. Further, an alternative proof of the conjecture raised by Akiyama, Egami and Tanigawa is also given.