Merge f369009 into b42421f

sympy/functions/elementary/exponential.py

@@ -827,5 +827,17 @@ def _eval_is_algebraic(self):
         else:
             return s.is_algebraic
 
+    def _eval_nseries(self, x, n, logx):
+        if len(self.args) == 1:
+            from sympy import O, Add, Integer, factorial
+            x = self.args[0]
+            o = O(x**n, x)
+            l = S.Zero
+            if n > 0:
+                l += Add(*[Integer(-k)**(k - 1)*x**k/factorial(k)
+                           for k in range(1, n)])
+            return l + o
+        return super(LambertW, self)._eval_nseries(x, n=n, logx=logx)
+
 
 from sympy.core.function import _coeff_isneg

sympy/functions/elementary/tests/test_exponential.py

@@ -1,5 +1,5 @@
 from sympy import (
-    symbols, log, Float, nan, oo, zoo, I, pi, E, exp, Symbol,
+    symbols, log, Float, nan, oo, zoo, I, pi, E, O, exp, Symbol,
     LambertW, sqrt, Rational, expand_log, S, sign, conjugate,
     sin, cos, sinh, cosh, tanh, exp_polar, re, Function, simplify)
 from sympy.abc import x, y, z
@@ -364,6 +364,10 @@ def test_lambertw():
     na = Symbol('na', nonzero=True, algebraic=True)
     assert LambertW(na).is_algebraic is False
 
+    # See sympy/sympy#7259:
+    assert LambertW(x).series(x) == x - x**2 + 3*x**3/2 - 8*x**4/3 + \
+        125*x**5/24 + O(x**6)
+
 
 def test_issue_5673():
     e = LambertW(-1)