Euler-Apéry Type Multiple Zeta Star Values and Multiple t-Star Values

By introducing an extra binomial factor in the summands of multiple zeta star series, we can define the Euler-Apéry type multiple zeta star series. Their convergent values at positive integers are called Euler-Apéry type multiple zeta star values. In this paper we establish several recurrence relations about these values and a parametric variant by the method of iterated integrals. We then find the explicit evaluations for some specific Euler-Apéry type multiple zeta star values and t-star values, together with a parametric variant of the star version.