diff --git a/rt-tests.lisp b/rt-tests.lisp
index 712b96cb85f14141a829945a137137bd8157c5dd..a4dac021efe5c544e9a5dcbf5c11b10dfd4bb516 100644
--- a/rt-tests.lisp
+++ b/rt-tests.lisp
@@ -1679,3 +1679,22 @@
       (check-accuracy 50.73 b true))
   nil)
 
+(rt:deftest bessel-j-complex.pos-order.d.2
+    (let ((b (bessel-j 1d0 #c(1d0 1)))
+	  (true #c(0.6141603349229036d0 0.3650280288270878d0)))
+      (check-accuracy 52.51 b true))
+  nil)
+
+(rt:deftest bessel-j-complex.pos-order.d.3
+    (let ((b (bessel-j 2d0 #c(1d0 1)))
+	  (true #c(0.0415798869439621d0 0.2473976415133063d0)))
+      (check-accuracy 50.41 b true))
+  nil)
+
+#+nil
+(rt:deftest bessel-j-complex.pos-order.d.4
+    (let ((b (bessel-j 2.3d0 #c(1d0 1)))
+	  (true #c(0.1920598664138632d0 -0.5158676904105332d0)))
+      (check-accuracy 53 b true))
+  nil)
+