How can I use "e" (Euler's number) and power operation in python 2.7

You can use exp(x) function of math library, which is same as e^x. Hence you may write your code as:

import math
x.append(1 - math.exp( -0.5 * (value1*value2)**2))

I have modified the equation by replacing 1/2 as 0.5. Else for Python <2.7, we'll have to explicitly type cast the division value to float because Python round of the result of division of two int as integer. For example: 1/2 gives 0 in python 2.7 and below.

Python's power operator is ** and Euler's number is math.e, so:

 from math import e
 x.append(1-e**(-value1**2/2*value2**2))

Just saying: numpy has this too. So no need to import math if you already did import numpy as np:

>>> np.exp(1)
2.718281828459045