These functions are in stan-math from from the PRs stan-dev/math#2792 and stan-dev/math#2797.

Let's expose them.

There is demand on the forums
https://discourse.mc-stan.org/t/gaussian-hypergeometric-function-for-exact-distribution-of-a-correlation/30606/3
https://discourse.mc-stan.org/t/hypergeometric-functions/252
https://discourse.mc-stan.org/t/confluent-hypergeometric-functions-to-estimate-population-size-and-detection-probability-from-spatially-replicated-counts/28758 (1F1 but still...)