Expressing the Hypergeometric Function $_3F_2(a,a,b;p,p;x) $ in terms of $_2F_1()$

Question

Is it possible to express the Clausen Hypergeometric Function $_3F_2(a,a,b;p,p;x)$ (the first two parameters and the last two are identical) in terms of the Gauss Hypergeometric Function $_2F_1()$ and Gamma function, with transformed arguments?

The reason that I would really like to do this, is because the variable $x$ is outside the range $0 \le x< 1$ in which the simple series expansion in terms of Pochhammer symbols is applicable. For the $_2F_1()$ function, I have a set of expansions with transformations for $x-$ values outside the range $0 \le x < 1$, following the paper "Computing the Hypergeometric Function" by Robert C. Forrey, Journal of Computational Physics, Vol. 137, #79, pp 79-100

Thanks

Answer 1

I need some help with a potential answer to my question:

Digging through Wolfram, I found the following:

where I'm assuming that the $\epsilon^{(2)}$ terms are some sort of series expansion coefficients of the $_3F_2$ function based on the parameters, and not the argument $z$. The site does not describe them in any detail. Any help here would be deeply appreciated.

Thanks

There is a result due to Choi and Hasanov that states

What is extremely unfortunate however, is that in my case, the element $\alpha_p < 0$ rendering this result inapplicable. Otherwise, this would've solved my problem, because it specifically reduces $_3F_2()$ to a summation of $_2F_1()$ which is exactly what I was seeking.