Expose hypergeometric_2F1 function

stan/math/fwd/fun.hpp

@@ -41,6 +41,7 @@
 #include <stan/math/fwd/fun/gamma_p.hpp>
 #include <stan/math/fwd/fun/gamma_q.hpp>
 #include <stan/math/fwd/fun/grad_inc_beta.hpp>
+#include <stan/math/fwd/fun/hypergeometric_2F1.hpp>
 #include <stan/math/fwd/fun/hypergeometric_pFq.hpp>
 #include <stan/math/fwd/fun/hypot.hpp>
 #include <stan/math/fwd/fun/inc_beta.hpp>

stan/math/fwd/fun/grad_inc_beta.hpp

@@ -41,9 +41,11 @@ void grad_inc_beta(fvar<T>& g1, fvar<T>& g2, fvar<T> a, fvar<T> b, fvar<T> z) {
   fvar<T> dF1 = 0;
   fvar<T> dF2 = 0;
   fvar<T> dF3 = 0;
+  fvar<T> dFz = 0;
 
-  if (value_of(value_of(C))) {
-    grad_2F1(dF1, dF2, dF3, a + b, fvar<T>(1.0), a + 1, z);
+  if (value_of_rec(C)) {
+    std::forward_as_tuple(dF1, dF2, dF3, dFz)
+        = grad_2F1<true>(a + b, fvar<T>(1.0), a + 1, z);
   }
 
   g1 = (c1 - 1.0 / a) * c3 + C * (dF1 + dF3);

stan/math/fwd/fun/hypergeometric_2F1.hpp

@@ -0,0 +1,65 @@
+#ifndef STAN_MATH_FWD_FUN_HYPERGEOMETRIC_2F1_HPP
+#define STAN_MATH_FWD_FUN_HYPERGEOMETRIC_2F1_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/fwd/core.hpp>
+#include <stan/math/prim/fun/hypergeometric_2F1.hpp>
+#include <stan/math/prim/fun/grad_2F1.hpp>
+
+namespace stan {
+namespace math {
+
+/**
+ * Returns the Gauss hypergeometric function applied to the
+ * input arguments:
+ * \f$_2F_1(a_1,a_2;b;z)\f$
+ *
+ * See 'grad_2F1.hpp' for the derivatives wrt each parameter
+ *
+ * @tparam Ta1 Type of scalar first 'a' argument
+ * @tparam Ta2 Type of scalar second 'a' argument
+ * @tparam Tb Type of scalar 'b' argument
+ * @tparam Tz Type of scalar 'z' argument
+ * @param[in] a1 First of 'a' arguments to function
+ * @param[in] a2 Second of 'a' arguments to function
+ * @param[in] b 'b' argument to function
+ * @param[in] z Scalar z argument
+ * @return Gauss hypergeometric function
+ */
+template <typename Ta1, typename Ta2, typename Tb, typename Tz,
+          require_all_stan_scalar_t<Ta1, Ta2, Tb, Tz>* = nullptr,
+          require_any_fvar_t<Ta1, Ta2, Tb, Tz>* = nullptr>
+inline return_type_t<Ta1, Ta1, Tb, Tz> hypergeometric_2F1(const Ta1& a1,
+                                                          const Ta2& a2,
+                                                          const Tb& b,
+                                                          const Tz& z) {
+  using fvar_t = return_type_t<Ta1, Ta1, Tb, Tz>;
+
+  auto a1_val = value_of(a1);
+  auto a2_val = value_of(a2);
+  auto b_val = value_of(b);
+  auto z_val = value_of(z);
+
+  auto grad_tuple = grad_2F1(a1, a2, b, z);
+
+  typename fvar_t::Scalar grad = 0;
+
+  if (!is_constant<Ta1>::value) {
+    grad += forward_as<fvar_t>(a1).d() * std::get<0>(grad_tuple);
+  }
+  if (!is_constant<Ta2>::value) {
+    grad += forward_as<fvar_t>(a2).d() * std::get<1>(grad_tuple);
+  }
+  if (!is_constant<Tb>::value) {
+    grad += forward_as<fvar_t>(b).d() * std::get<2>(grad_tuple);
+  }
+  if (!is_constant<Tz>::value) {
+    grad += forward_as<fvar_t>(z).d() * std::get<3>(grad_tuple);
+  }
+
+  return fvar_t(hypergeometric_2F1(a1_val, a2_val, b_val, z_val), grad);
+}
+
+}  // namespace math
+}  // namespace stan
+#endif

stan/math/prim/fun.hpp

@@ -129,8 +129,9 @@
 #include <stan/math/prim/fun/grad_reg_inc_gamma.hpp>
 #include <stan/math/prim/fun/grad_reg_lower_inc_gamma.hpp>
 #include <stan/math/prim/fun/head.hpp>
-#include <stan/math/prim/fun/hypergeometric_pFq.hpp>
+#include <stan/math/prim/fun/hypergeometric_2F1.hpp>
 #include <stan/math/prim/fun/hypergeometric_2F2.hpp>
+#include <stan/math/prim/fun/hypergeometric_pFq.hpp>
 #include <stan/math/prim/fun/hypot.hpp>
 #include <stan/math/prim/fun/identity_constrain.hpp>
 #include <stan/math/prim/fun/identity_free.hpp>