Merge pull request sympy#17849 from czgdp1807/pr-12116

jksuom · web-flow · commit 3f687d2f8bb2 · 2019-11-11T19:57:13.000+02:00
Added `eval` in sympy.functions.special.bessel.jn
diff --git a/sympy/functions/special/bessel.py b/sympy/functions/special/bessel.py
@@ -668,6 +668,18 @@ class jn(SphericalBesselBase):
     .. [1] http://dlmf.nist.gov/10.47
 
     """
+    @classmethod
+    def eval(cls, nu, z):
+        if z.is_zero:
+            if nu.is_zero:
+                return S.One
+            elif nu.is_integer:
+                if nu.is_positive:
+                    return S.Zero
+                else:
+                    return S.ComplexInfinity
+        if z in (S.NegativeInfinity, S.Infinity):
+            return S.Zero
 
     def _rewrite(self):
         return self._eval_rewrite_as_besselj(self.order, self.argument)
diff --git a/sympy/functions/special/tests/test_bessel.py b/sympy/functions/special/tests/test_bessel.py
@@ -221,6 +221,13 @@ def myn(n, z):
 
 def test_jn():
     z = symbols("z")
+    assert jn(0, 0) == 1
+    assert jn(1, 0) == 0
+    assert jn(-1, 0) == S.ComplexInfinity
+    assert jn(z, 0) == jn(z, 0, evaluate=False)
+    assert jn(0, oo) == 0
+    assert jn(0, -oo) == 0
+
     assert mjn(0, z) == sin(z)/z
     assert mjn(1, z) == sin(z)/z**2 - cos(z)/z
     assert mjn(2, z) == (3/z**3 - 1/z)*sin(z) - (3/z**2) * cos(z)
