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Once the 2F1 is in, I'll also be working these up (if you haven't started already!). Since the gamma_p_inv and gamma_q_inv gradients involve a $_2F_2(a,a; a+1,a+1)$ call, which we can express using the 1F1 (eqn. 24 in this paper). Note that the identity still requires a call to $_2F_2(1,1; 2,2)$ , but this can also be represented pretty trivially in closed form
Boost has both of these functions.
The hypergeometric 1F1 function is interesting in that the lower incomplete gamma function can be expressed as
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