diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
index 56ac9ead39..238297aba0 100644
--- a/include/boost/math/distributions/non_central_beta.hpp
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -86,7 +86,12 @@ namespace boost
                }
                pois *= i / l2;
                beta += xterm;
-               xterm *= (a + i - 1) / (x * (a + b + i - 2));
+
+               if (a + b + i != 2)
+               {
+                  xterm *= (a + i - 1) / (x * (a + b + i - 2));
+               }
+               
                last_term = term;
             }
             for(int i = k + 1; ; ++i)
@@ -555,7 +560,11 @@ namespace boost
                   break;
                }
                pois *= i / l2;
-               beta *= (a + i - 1) / (x * (a + i + b - 1));
+
+               if (a + b + i != 1)
+               {
+                  beta *= (a + i - 1) / (x * (a + i + b - 1));
+               }
             }
             for(int i = k + 1; ; ++i)
             {
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 57295797ff..1a555a3fc4 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -891,6 +891,7 @@ test-suite distribution_tests :
 
    [ compile test_dist_deduction_guides.cpp : [ requires cpp_deduction_guides cpp_variadic_templates ] ]
    [ run git_issue_800.cpp ../../test/build//boost_unit_test_framework  ]
+   [ run git_issue_845.cpp ../../test/build//boost_unit_test_framework  ]
 ;
 
 test-suite mp :
diff --git a/test/git_issue_845.cpp b/test/git_issue_845.cpp
new file mode 100644
index 0000000000..d49a5ddf4e
--- /dev/null
+++ b/test/git_issue_845.cpp
@@ -0,0 +1,59 @@
+// Copyright Matt Borland, 2022
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0. (See accompanying file
+// LICENSE or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <cfenv>
+#include <iostream>
+#include <boost/math/distributions/non_central_f.hpp>
+#include "math_unit_test.hpp"
+
+#pragma STDC FENV_ACCESS ON
+
+int main() 
+{
+    auto ncf1 = boost::math::non_central_f(2, 2, 2);
+    const auto cdf1 = boost::math::cdf(ncf1, 0.05);
+
+    // https://www.wolframalpha.com/input?i=N%5BCdf%28NonCentralFRatioDistribution%282%2C2%2C2%29%2C+0.05%29%2C+15%5D
+    CHECK_ULP_CLOSE(cdf1, 0.0183724431823392, 15);
+
+    if (std::fetestexcept(FE_INVALID) || std::fetestexcept(FE_DIVBYZERO)) 
+    {
+        return 1;
+    }
+
+    auto ncf2 = boost::math::non_central_f(1, 3, 2);
+    const auto cdf2 = boost::math::cdf(ncf2, 0.05);
+
+    // https://www.wolframalpha.com/input?i=N%5BCdf%28NonCentralFRatioDistribution%281%2C3%2C2%29%2C+0.05%29%2C+15%5D
+    CHECK_ULP_CLOSE(cdf2, 0.0611253404710995, 15);
+
+    if (std::fetestexcept(FE_INVALID) || std::fetestexcept(FE_DIVBYZERO))
+    {
+        return 2;
+    }
+
+    auto ncf3 = boost::math::non_central_f(1, 1, 2);
+    const auto cdf3 = boost::math::cdf(ncf3, 0.05);
+
+    // https://www.wolframalpha.com/input?i=N%5BCdf%28NonCentralFRatioDistribution%281%2C1%2C2%29%2C+0.05%29%2C+15%5D
+    CHECK_ULP_CLOSE(cdf3, 0.0531991288870987, 15);
+
+    if (std::fetestexcept(FE_INVALID) || std::fetestexcept(FE_DIVBYZERO))
+    {
+        return 3;
+    }
+
+    const auto pdf3 = boost::math::pdf(ncf3, 0.05);
+
+    // https://www.wolframalpha.com/input?i=N%5BPdf%28NonCentralFRatioDistribution%281%2C1%2C2%29%2C+0.05%29%2C+15%5D
+    CHECK_ULP_CLOSE(pdf3, 0.547785080683644, 15);
+
+    if (std::fetestexcept(FE_INVALID) || std::fetestexcept(FE_DIVBYZERO))
+    {
+        return 4;
+    }
+
+    return boost::math::test::report_errors();
+}