diff -r -U2 sympy-1.0.orig/sympy/functions/special/tests/test_zeta_functions.py sympy-1.0/sympy/functions/special/tests/test_zeta_functions.py
--- sympy-1.0.orig/sympy/functions/special/tests/test_zeta_functions.py	2016-03-09 00:38:39.000000000 +0600
+++ sympy-1.0/sympy/functions/special/tests/test_zeta_functions.py	2016-12-28 23:25:19.370041561 +0700
@@ -125,5 +125,5 @@
     assert polylog(s, 0) == 0
     assert polylog(s, 1) == zeta(s)
-    assert polylog(s, -1) == dirichlet_eta(s)
+    assert polylog(s, -1) == -dirichlet_eta(s)
 
     assert myexpand(polylog(1, z), -log(1 + exp_polar(-I*pi)*z))
diff -r -U2 sympy-1.0.orig/sympy/functions/special/zeta_functions.py sympy-1.0/sympy/functions/special/zeta_functions.py
--- sympy-1.0.orig/sympy/functions/special/zeta_functions.py	2016-03-09 00:38:39.000000000 +0600
+++ sympy-1.0/sympy/functions/special/zeta_functions.py	2016-12-28 23:23:56.109047180 +0700
@@ -245,5 +245,5 @@
     zeta(s)
     >>> polylog(s, -1)
-    dirichlet_eta(s)
+    -dirichlet_eta(s)
 
     If :math:`s` is a negative integer, :math:`0` or :math:`1`, the
@@ -272,10 +272,17 @@
     @classmethod
     def eval(cls, s, z):
+        from sympy import unpolarify
         if z == 1:
             return zeta(s)
         elif z == -1:
-            return dirichlet_eta(s)
+            return -dirichlet_eta(s)
         elif z == 0:
-            return 0
+            return S.Zero
+
+        # branch handling
+        if (1 - abs(z)).is_nonnegative:
+            newz = unpolarify(z)
+            if newz != z:
+                return cls(s, newz)
 
     def fdiff(self, argindex=1):
@@ -486,5 +493,5 @@
     For `\operatorname{Re}(s) > 0`, this function is defined as
 
-    .. math:: \eta(s) = \sum_{n=1}^\infty \frac{(-1)^n}{n^s}.
+    .. math:: \eta(s) = \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n^s}.
 
     It admits a unique analytic continuation to all of :math:`\mathbb{C}`.