As part of a broader fractional integral calculation using the Riemann-Liouville operator, I encountered the following integral:
$$f(z,h,a) = \int_0^z\, \frac{h^{1-u}}{u-1}\cdot(z-u)^{a-1}\, du \qquad z \in \mathbb{C}. h,a \in \mathbb{R}$$
Could this integral be simplified further, e.g. by expressing it into a Hypergeometric function? I have tried Wolfram Math, but without any success. A complicating factor might be that when $z \in \mathbb{R}, z>1$, a pole will be induced in the integrand.