Generalized the q-Digamma and the q-Polygamma Functions via Neutrices

The q-digamma function psi(q)(x) and the q-polygamma functions psi((r))(q) (x), r is an element of N = {1,2,...} are defined for all x > 0 and 0 < q < 1. In this paper, the neutrices and the neutrix limit are used to define the q-digamma function psi(q)(x) and the q-polygamma functions psi((r))(q) (x), r is an element of N for all x is an element of R. Moreover, further results are given.