Hello Mathematicians :)

I'm currently investigating the two (related, generalised, unnormalised) functions

$$f(x)\equiv x^{a+\frac{1}{2}} e^{-qx^b}{}_1F_1\left(c;d;2qx^b\right) \hspace{4mm} \textrm{and} \hspace{4mm} \tilde{f}(x)\equiv x^{-a+\frac{1}{2}} e^{-qx^b}{}_1F_1\left(\tilde{c};\tilde{d};2qx^b\right)$$

where $a$ is positive and usually set $=\frac{1}{2}$, although this not being the case is also considered.

I was wondering if anyone could please provide me with a lead as to where I may find the Green's functions of $f(x)$ and $\tilde{f}(x)$? Sadly I have not been able to achieve the result through my own computations and an internet / handbook / library search has turned up nothing which I have been able to use

I would be forever indebted to anyone who could provide a reference where I may find these identities

Many thanks :)