  We consider the q-hypergeometric equation with q^{N}=1 and $\alpha, \beta,
\gamma \in {\Bbb Z}$. We solve this equation on the space of functions given by
a power series multiplied by a power of the logarithmic function. We prove that
the subspace of solutions is two-dimensional over the field of quasi-constants.
We get a basis for this space explicitly. In terms of this basis, we represent
the q-hypergeometric function of the Barnes type constructed by Nishizawa and
Ueno. Then we see that this function has logarithmic singularity at the origin.
This is a difference between the q-hypergeometric functions with 0<|q|<1 and at
|q|=1.
