Index: boost/math/special_functions/detail/bessel_jn.hpp
===================================================================
--- boost/math/special_functions/detail/bessel_jn.hpp	(revision 51047)
+++ boost/math/special_functions/detail/bessel_jn.hpp	(working copy)
@@ -32,9 +32,12 @@
     {
         return bessel_j0(x);
     }
-    if (n == 1)
+    if ((n == 1) || (n == -1))
     {
-        return bessel_j1(x);
+        factor = n;  // J_{-1}(z) = -1*J_1(z)
+        value = bessel_j1(x);
+        value *=factor;
+        return value;
     }
     if (n < 0)
     {