Meromorphic continuation of a q-analogue of multiple zeta function

In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we locate the poles of the function and the corresponding residues. While locating the poles, we also obtain an inverse of an infinite triangular matrix in a particular case.

💡 Research Summary

The paper addresses the problem of extending the q‑analogue of the multiple zeta function, denoted ζ_q(s₁,…,s_r), to a meromorphic function on the whole complex space C^r. After recalling the definition of the q‑integer