convol poly

from numpy import linspace
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from fractions import Fraction

W = [Fraction(1)]
def W2p1(n):
    global W
    for i in range(len(W), n+1):
        W.append(Fraction(2*i, 2*i+1)*W[i-1])
    return W[n]

def phi(n, x): return (1-x**2)**n/2/W2p1(n).real

def init():
    line.set_data([], [])
    return line,

def animate(i):
    line.set_data(pts, phi(i, pts))
    return line,
##
W2p1(600) # Pre-compute Wallis
pts = linspace(-1, 1, 1000)
line, = plt.plot([], [])
plt.axis([-1, 1, -1, 15])
plt.show()

## Animation
anim = FuncAnimation(plt.gcf(), animate, init_func=init, frames=600, interval=16, blit=True, repeat=False)

## All together
for i in range(1, 600): plt.plot(pts, phi(i, pts))
plt.show()