diff --git a/stan/math/prim/fun/hypergeometric_3F2.hpp b/stan/math/prim/fun/hypergeometric_3F2.hpp
index 4508e3b4c84..5f5dbedea69 100644
--- a/stan/math/prim/fun/hypergeometric_3F2.hpp
+++ b/stan/math/prim/fun/hypergeometric_3F2.hpp
@@ -12,6 +12,7 @@
 #include <stan/math/prim/fun/sum.hpp>
 #include <stan/math/prim/fun/sign.hpp>
 #include <stan/math/prim/fun/value_of_rec.hpp>
+#include <stan/math/prim/fun/log_sum_exp_signed.hpp>
 
 namespace stan {
 namespace math {
@@ -30,7 +31,7 @@ T_return hypergeometric_3F2_infsum(const Ta& a, const Tb& b, const Tz& z,
   check_3F2_converges("hypergeometric_3F2", a_array[0], a_array[1], a_array[2],
                       b_array[0], b_array[1], z);
 
-  T_return t_acc = 1.0;
+  T_return t_acc = 0.0;
   T_return log_t = 0.0;
   T_return log_z = log(fabs(z));
   Eigen::ArrayXi a_signs = sign(value_of_rec(a_array));
@@ -39,7 +40,7 @@ T_return hypergeometric_3F2_infsum(const Ta& a, const Tb& b, const Tz& z,
   plain_type_t<decltype(b_array)> bpk = b_array;
   int z_sign = sign(value_of_rec(z));
   int t_sign = z_sign * a_signs.prod() * b_signs.prod();
-
+  int acc_sign = 1;
   int k = 0;
   while (k <= max_steps && log_t >= log(precision)) {
     // Replace zero values with 1 prior to taking the log so that we accumulate
@@ -52,7 +53,8 @@ T_return hypergeometric_3F2_infsum(const Ta& a, const Tb& b, const Tz& z,
     }
 
     log_t += p + log_z;
-    t_acc += t_sign * exp(log_t);
+    std::forward_as_tuple(t_acc, acc_sign)
+      = log_sum_exp_signed(t_acc, acc_sign, log_t, t_sign);
 
     if (is_inf(t_acc)) {
       throw_domain_error("hypergeometric_3F2", "sum (output)", t_acc,
@@ -70,7 +72,7 @@ T_return hypergeometric_3F2_infsum(const Ta& a, const Tb& b, const Tz& z,
                        "exceeded  iterations, hypergeometric function did not ",
                        "converge.");
   }
-  return t_acc;
+  return acc_sign * exp(t_acc);
 }
 }  // namespace internal
 
@@ -109,7 +111,8 @@ T_return hypergeometric_3F2_infsum(const Ta& a, const Tb& b, const Tz& z,
  * @param[in] z z (is always called with 1 from beta binomial cdfs)
  * @param[in] precision precision of the infinite sum. defaults to 1e-6
  * @param[in] max_steps number of steps to take. defaults to 1e5
- * @return Generalized hypergeometric function applied to the inputs
+ * The 3F2 generalized hypergeometric function applied to the
+ *  arguments {a1, a2, a3}, {b1, b2}
  */
 template <typename Ta, typename Tb, typename Tz,
           require_all_vector_t<Ta, Tb>* = nullptr,
diff --git a/stan/math/prim/fun/log_sum_exp_signed.hpp b/stan/math/prim/fun/log_sum_exp_signed.hpp
index 196093eb3c5..97a74ac4407 100644
--- a/stan/math/prim/fun/log_sum_exp_signed.hpp
+++ b/stan/math/prim/fun/log_sum_exp_signed.hpp
@@ -4,7 +4,8 @@
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/constants.hpp>
 #include <stan/math/prim/fun/Eigen.hpp>
-#include <stan/math/prim/fun/log1p_exp.hpp>
+#include <stan/math/prim/fun/log_diff_exp.hpp>
+#include <stan/math/prim/fun/log_sum_exp.hpp>
 #include <cmath>
 #include <vector>