Some evaluation of q-analogues of Euler sums

In this paper, we discuss the analytic representations of q-Euler sums which involve q-harmonic numbers through q-polylogarithms, either linearly or nonlinearly, and give explicit formulae for several classes of q-Euler sums in terms of q-polylogarithms and q-special functions. Furthermore, we develop new closed form representations of sums of quadratic and cubic parametric q-Euler sums. Finally, we can find that the q-Euler sums are reducible to the classical Euler sums when q approaches 1.