Asymptotic Behaviors of Hypergeometric function for two large parameters

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I am studying the asymptotic behaviors of the hypergeometric function ${}_2F_1(a,b;c;z)$ by reading this paper. However, the paper does not mention the case when $b$ and $c$ are large. I tried looking online for sources that would consider the case I am interested in. What would be the asymptotic formula for this case?