Sage code for Krawtchouk K10, K11 (q=3 and n=150)
def K(n,q,i,x):
return sum( (-1)^j * (q-1)^(i-j) * binomial(x,j) * binomial(n-x,i-j) for j in [0..i])
def K1(n,q,i,x):
return K(n,q,i,x) * sqrt((q-1)^x * factorial(n) / (q^n * factorial(x)*factorial(n-x)))
def K2(n,q,i,x):
return K1(n,q,i,x) / sqrt((q-1)^i * binomial(n,i))
def f10(x):
return K2(150.,3,10,x)
def f11(x):
return K2(150.,3,11,x)
H10 = plot(f10,(x,0,150),plot_points=2000,color="red")
H11 = plot(f11,(x,0,150),plot_points=2000,color="blue")
(H10+H11).show()