DOC: fix conflicting ewma documentation

doc/source/computation.rst

@@ -450,7 +450,7 @@ average as
 
 .. math::
 
-    y_t = \alpha y_{t-1} + (1 - \alpha) x_t
+    y_t = (1 - \alpha) y_{t-1} + \alpha x_t
 
 One must have :math:`0 < \alpha \leq 1`, but rather than pass :math:`\alpha`
 directly, it's easier to think about either the **span** or **center of mass
@@ -461,9 +461,19 @@ directly, it's easier to think about either the **span** or **center of mass
    \alpha =
     \begin{cases}
 	\frac{2}{s + 1}, s = \text{span}\\
-	\frac{1}{c + 1}, c = \text{center of mass}
+	\frac{1}{1 + c}, c = \text{center of mass}
     \end{cases}
 
+.. note::
+
+  the equation above is sometimes written in the form
+
+  .. math::
+
+    y_t = \alpha' y_{t-1} + (1 - \alpha') x_t
+
+  where :math:`\alpha' = 1 - \alpha`.
+
 You can pass one or the other to these functions but not both. **Span**
 corresponds to what is commonly called a "20-day EW moving average" for
 example. **Center of mass** has a more physical interpretation. For example,

pandas/stats/moments.py

@@ -56,9 +56,9 @@
 ----------
 %s
 com : float. optional
-    Center of mass: \alpha = com / (1 + com),
+    Center of mass: :math:`\alpha = 1 / (1 + com)`,
 span : float, optional
-    Specify decay in terms of span, \alpha = 2 / (span + 1)
+    Specify decay in terms of span, :math:`\alpha = 2 / (span + 1)`
 min_periods : int, default 0
     Number of observations in sample to require (only affects
     beginning)
@@ -75,8 +75,8 @@
 Either center of mass or span must be specified
 
 EWMA is sometimes specified using a "span" parameter s, we have have that the
-decay parameter \alpha is related to the span as
-:math:`\alpha = 1 - 2 / (s + 1) = c / (1 + c)`
+decay parameter :math:`\alpha` is related to the span as
+:math:`\alpha = 2 / (s + 1) = 1 / (1 + c)`
 
 where c is the center of mass. Given a span, the associated center of mass is
 :math:`c = (s - 1) / 2`