import numpy as np
import time

#grenser
b=2
st = time.time()

#gitter, n må være partall
n=20
theta=np.pi*np.linspace(0,1,n)

x=(1+np.cos(theta))/2


theta = theta[1:n-1]
v=np.ones(n-2)
w=np.zeros(n)

for k in range(int(n/2-1)):
    v = v - 2*np.cos(2*(k+1)*theta)/(4*(k+1)**2-1)


w[1:n-1] = 2*v/(n-1)

w[0]=1/(n-1)**2
w[n-1]=w[0]

p = b*np.dot(w,np.exp(-(b*x)**2/2))/np.sqrt(2*np.pi)/2

et = time.time()


print(f'p={p}')
print(f'n={n} tok {et-st:.3f} sekunder')