diff --git a/stan/math/prim/fun/hypergeometric_2F1.hpp b/stan/math/prim/fun/hypergeometric_2F1.hpp
index ae327e033f1..730be40fc45 100644
--- a/stan/math/prim/fun/hypergeometric_2F1.hpp
+++ b/stan/math/prim/fun/hypergeometric_2F1.hpp
@@ -16,7 +16,7 @@
 #include <stan/math/prim/fun/pow.hpp>
 #include <stan/math/prim/fun/sqrt.hpp>
 #include <stan/math/prim/fun/square.hpp>
-#include <stan/math/prim/fun/hypergeometric_pFq.hpp>
+#include <stan/math/prim/fun/hypergeometric_pFq_helper.hpp>
 #include <boost/optional.hpp>
 
 namespace stan {
@@ -187,7 +187,7 @@ inline return_type_t<Ta1, Ta2, Tb, Tz> hypergeometric_2F1(const Ta1& a1,
 
     a_args << a1, a2;
     b_args << b;
-    return hypergeometric_pFq(a_args, b_args, z);
+    return internal::hypergeometric_pFq_helper(a_args, b_args, z);
   } catch (const std::exception& e) {
     // Apply Euler's hypergeometric transformation if function
     // will not converge with current arguments
@@ -200,7 +200,8 @@ inline return_type_t<Ta1, Ta2, Tb, Tz> hypergeometric_2F1(const Ta1& a1,
 
     a_args << a1_t, a2_t;
     b_args << b_t;
-    return hypergeometric_pFq(a_args, b_args, z_t) / pow(1 - z, a2);
+    return internal::hypergeometric_pFq_helper(a_args, b_args, z_t)
+           / pow(1 - z, a2);
   }
 }
 }  // namespace math
diff --git a/stan/math/prim/fun/hypergeometric_pFq.hpp b/stan/math/prim/fun/hypergeometric_pFq.hpp
index c2b30610314..65b387b3f3c 100644
--- a/stan/math/prim/fun/hypergeometric_pFq.hpp
+++ b/stan/math/prim/fun/hypergeometric_pFq.hpp
@@ -4,12 +4,14 @@
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err/check_not_nan.hpp>
 #include <stan/math/prim/err/check_finite.hpp>
+#include <stan/math/prim/fun/to_array_1d.hpp>
 #include <stan/math/prim/fun/to_row_vector.hpp>
-#include <boost/math/special_functions/hypergeometric_pFq.hpp>
+#include <stan/math/prim/fun/hypergeometric_1F0.hpp>
+#include <stan/math/prim/fun/hypergeometric_2F1.hpp>
+#include <stan/math/prim/fun/hypergeometric_pFq_helper.hpp>
 
 namespace stan {
 namespace math {
-
 /**
  * Returns the generalized hypergeometric function applied to the
  * input arguments:
@@ -29,6 +31,13 @@ return_type_t<Ta, Tb, Tz> hypergeometric_pFq(const Ta& a, const Tb& b,
                                              const Tz& z) {
   plain_type_t<Ta> a_ref = a;
   plain_type_t<Tb> b_ref = b;
+
+  if (a_ref.size() == 1 && b_ref.size() == 0) {
+    return hypergeometric_1F0(a_ref[0], z);
+  } else if (a_ref.size() == 2 && b_ref.size() == 1) {
+    return hypergeometric_2F1(a_ref[0], a_ref[1], b_ref[0], z);
+  }
+
   check_finite("hypergeometric_pFq", "a", a_ref);
   check_finite("hypergeometric_pFq", "b", b_ref);
   check_finite("hypergeometric_pFq", "z", z);
@@ -50,9 +59,7 @@ return_type_t<Ta, Tb, Tz> hypergeometric_pFq(const Ta& a, const Tb& b,
     throw std::domain_error(msg.str());
   }
 
-  return boost::math::hypergeometric_pFq(
-      std::vector<double>(a_ref.data(), a_ref.data() + a_ref.size()),
-      std::vector<double>(b_ref.data(), b_ref.data() + b_ref.size()), z);
+  return internal::hypergeometric_pFq_helper(a_ref, b_ref, z);
 }
 }  // namespace math
 }  // namespace stan
diff --git a/stan/math/prim/fun/hypergeometric_pFq_helper.hpp b/stan/math/prim/fun/hypergeometric_pFq_helper.hpp
new file mode 100644
index 00000000000..8867f316c3c
--- /dev/null
+++ b/stan/math/prim/fun/hypergeometric_pFq_helper.hpp
@@ -0,0 +1,32 @@
+#ifndef STAN_MATH_PRIM_FUN_HYPERGEOMETRIC_PFQ_HELPER_HPP
+#define STAN_MATH_PRIM_FUN_HYPERGEOMETRIC_PFQ_HELPER_HPP
+
+#include <stan/math/prim/meta.hpp>
+#include <stan/math/prim/fun/to_array_1d.hpp>
+#include <boost/math/special_functions/hypergeometric_pFq.hpp>
+
+namespace stan {
+namespace math {
+namespace internal {
+/**
+ * Implementation for calculating the generalized hypergeometric function
+ * \f$_pF_q(a_1,...,a_p;b_1,...,b_q;z)\f$.
+ *
+ * This is declared separatel to avoid circular dependencies between the
+ * various hypergeometric functions.
+ *
+ * @param[in] a Vector of 'a' arguments to function
+ * @param[in] b Vector of 'b' arguments to function
+ * @param[in] z Scalar z argument
+ * @return Generalized hypergeometric function
+ */
+template <typename Ta, typename Tb, typename Tz,
+          require_all_vector_st<std::is_arithmetic, Ta, Tb>* = nullptr,
+          require_arithmetic_t<Tz>* = nullptr>
+inline double hypergeometric_pFq_helper(const Ta& a, const Tb& b, const Tz& z) {
+  return boost::math::hypergeometric_pFq(to_array_1d(a), to_array_1d(b), z);
+}
+}  // namespace internal
+}  // namespace math
+}  // namespace stan
+#endif