I wonder whether there is some general algorithm or strategy to try to write some general function in terms of the H-function.
For instance, consider the following function. $$ f(x)=\alpha^{k x} \frac{x^{\beta}}{[\Gamma(x)]^{n}}, $$ where $\alpha\beta\in\mathbb{R}^+$ and $k,n\in \mathbb{N}^+$. I am trying to obtain some H-function of the form $$ f(x)=x^{\beta}\times H(g(x)), $$ where $H$ is the Fox H-function and $g(x)$ some function of $x$. I would appreciate any directions that could help me. Thanks in advance.