Onq-analogues of quadratic Euler sums

摘要

In this paper we studyq-analogues of Euler sums and present a new family of identities by using the method of Jacksonq-integral representations of series. We then apply it to obtain a family of identities relating quadratic Euler sums to linear sums andq-polylogarithms. Furthermore, we use certain stuffle products to evaluate severalq-series withq-harmonic numbers. Some interesting new results and illustrative examples are considered. Finally, ifqtends to 1, we obtain some explicit relations for the classical Euler sums.