I have a hypergeometric function that looks like the following:
$$ G(x) = {}_p F_p (a, a, a, ..., a; a+1, a+1, a+1, ..., a+1; -i C x), $$ where $p > 1$, $a, C > 0$, and $i = \sqrt{-1}$.
In literature, it is known that the function converges for all $x$ in this case as here the condition $p < q+1$ is satisfied for a generic hypergeometric function $_pF_q$, and the radius of convergence is $\infty$.
So, what does this series converge to? I assume that the software computes this directly?