How does a software (e.g., MATLAB) compute the value of a hypergeometric series that converges?

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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?