LAUSR

The purpose of this paper is the presentation of an identity which is closely related to the sum relation involving multiple zeta star values with even arguments. Let $$E^{\star }(m,n,k)$$E⋆(m,n,k) be the sum of all multiple zeta star values of depth k and weight mn with arguments multiples of $$m\ge 2$$m≥2. In this paper, we give two formulas for $$E^{\star }(2s,n,k)$$E⋆(2s,n,k) for $$s=1,2,3$$s=1,2,3 and in particular, by comparing the two we obtain a Bernoulli numbers identity. There are corresponding results included in a special kind of alternating multiple zeta values.