# -*- coding: utf-8 -*-
"""
Created on Wed Jan 07 14:43:25 2015

@author: grivet
Listing 7.1 : Polynômes de Laguerre calculés par 
récurrence ou tirés de la bibliothèque Scipy

"""
import numpy as np
from scipy.special import *
import matplotlib.pyplot as plt
def L(n,x):
    if n == 0:
        return 1
    elif n == 1:
        return 1-x
    else:
        k = 1; Lavder = 1; Lder = 1-x
        while k < n:
            L = ((2*k+1-x)*Lder - k*Lavder)/(k+1)
            Lavder = Lder
            Lder = L
            k += 1
        return L

x = np.linspace(0,6,100)
plt.plot(x,L(5,x),label="n = 5")
plt.plot(x,L(4,x),label="n = 4")
plt.plot(x,L(3,x),label="n = 3")
#plt.plot(x,zeros_like(x),'-k')
plt.title('Polynomes de Laguerre, n = 3,4,5,6')
plt.xlabel('$x$',fontsize=20)
plt.ylabel('$L_n(x)$',fontsize=20)
plt.plot(x,eval_laguerre(6,x),label="n = 6")
plt.show()
plt.legend()