where all s_{j} are non-zero integers and
A non-alternating Euler sum (i.e., all a_{j}=1) is called a
Multiple zeta value (MZV).
Additionally, for non-negative integers
and complex p with ,
we define
which reduces to an MZV when p=1.
We have found it interesting to look at the case when
.
We call these sums Multiple Clausen values (MCVs) and write:
It is convenient to separate these MCVs into real and imaginary parts. This is done according to the following scheme:
Note that when k = 1, mcl and mgl reduce to the values of the classical Clausen and Glaisher functions (as described in Lewin) at
.