EasyCalculusca-102

Legendre Polynomial Value

Problem

Evaluate the Legendre polynomial P_n(x) with the Bonnet recurrence:

P_0 = 1, P_1 = x, and (k+1) * P_{k+1} = (2k+1) * x * P_k - k * P_{k-1}

Assume n >= 0.

Hint

Carry the two previous polynomials and apply the three-term recurrence.

case 1

in: [0,0.5]

expected: 1

case 2

in: [1,0.5]

expected: 0.5

case 3

in: [2,0.5]

expected: -0.125

case 4

in: [3,1]

expected: 1

case 5

in: [4,0.5]

expected: -0.2890625

Starter codePython

def legendre_p(n, x):
    # Your code here
    pass

5 test cases · run your code against them in the editor