Add test case.

test/Jamfile.v2

@@ -192,6 +192,7 @@ test-suite special_fun :
    [ run git_issue_184.cpp ]
    [ run git_issue_1137.cpp ]
    [ run git_issue_1139.cpp ]
+   [ run git_issue_1175.cpp ]
    [ run special_functions_test.cpp /boost/test//boost_unit_test_framework  ]
    [ run test_airy.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework  ]
    [ run test_bessel_j.cpp test_instances//test_instances pch_light /boost/test//boost_unit_test_framework  ]

test/git_issue_1175.cpp

@@ -0,0 +1,25 @@
+//  (C) Copyright Matt Borland 2023.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include "math_unit_test.hpp"
+#include <iostream>
+#include <boost/math/distributions/beta.hpp>
+
+using namespace std;
+using boost::math::beta_distribution;
+
+int main(int argc, char* argv[])
+{
+   double a = 5.0;
+   double b = 5.0;
+   double p = 0.5;
+
+   beta_distribution<> dist(a, b);
+   double x = quantile(dist, p);
+
+   CHECK_ULP_CLOSE(x, 0.5, 2);
+
+   return boost::math::test::report_errors();
+}