Arithmetic operations (+, -, /, *, and so on) can be applied either to a Series or between two Series objects. When applied to a single Series, the operation is applied to all of the values in that Series. The following code demonstrates arithmetic operations applied to a Series object by multiplying the values in s3 by 2. The result is a new Series with the new values (s3 is unchanged).
In [46]: # multiply all values in s3 by 2 s3 * 2 Out[46]: a 2 b 4 c 6 dtype: int64
The preceding code is also roughly equivalent to the following code, which creates a new series from a scalar value using the index from s3. It has the same result, but it is not as efficient, as alignment is performed between the Series objects instead of a simple vectorization of the multiplication:
In [47]: # scalar series using s3's index t = pd.Series(2, s3.index) s3 * t Out[47]: a 2 b 4 c 6 dtype: int64