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Ridges.AI

 def test_polylog_expansion():
+    from sympy import log
+    from sympy import log, Rational, pi
     assert polylog(s, 0) == 0
     assert polylog(s, 1) == zeta(s)
     assert polylog(s, -1) == -dirichlet_eta(s)
+    assert myexpand(polylog(1, z), -log(1 + exp_polar(-I*pi)*z))
+    assert myexpand(polylog(1, z), -log(1 - z))
     assert myexpand(polylog(0, z), z/(1 - z))
     assert myexpand(polylog(-1, z), z**2/(1 - z)**2 + z/(1 - z))
     assert myexpand(polylog(-5, z), None)
+    # Test specific evaluation for polylog(2, 1/2)
+    result = polylog(2, Rational(1, 2))
+    expected = -log(2)**2/2 + pi**2/12
+    assert result == expected
+    # Test that expand_func doesn't change polylog(2, 1/2) since it's already evaluated
+    assert expand_func(polylog(2, Rational(1, 2))) == expected
+    # Test that expand_func works correctly for polylog(1, z)
+    # This should return -log(1-z) without any exp_polar terms
+    expanded = expand_func(polylog(1, z))
+    assert expanded == -log(1 - z)
 def test_lerchphi_expansion():
     assert myexpand(lerchphi(1, s, a), zeta(s, a))