mcloren_mult_sin.py

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

xs = np.arange(-100, 100, 0.1)
ys = np.sin(xs)

n = 75

def mcloren(x):
    result = 0
    for i in range(n):
        result += (-1)**i * (x**(2*i + 1)) / np.math.factorial(2*i + 1)
    return result

def mult(x):
    result = x
    for i in range(n-1):
        result *= 1 - (x / ((i+1) * np.pi)) ** 2
    return result

ys_mc = np.vectorize(mcloren)(xs)
ys_mp = np.vectorize(mult)(xs)

plt.ylim(ymin=-2, ymax=2)
plt.plot(xs, ys)
plt.plot(xs, ys_mc)
plt.plot(xs, ys_mp)