xmin = -1000000
xmax = 1000000
dx = 1
x = np.arange(xmin, xmax + dx, dx)
gx = 2 / np.sqrt(3) * np.pi ** -0.25 * (1 - x ** 2) * np.exp(-x ** 2 / 2)
sum_gx = np.trapz(gx, x, dx)
Infinite Summation in Python