# How to derive Legendre Polynomials?

1. Nov 11, 2014

### terp.asessed

• Note that filling in the attempt at solution is mandatory.
1. The problem statement, all variables and given/known data
Could someone explain how Legendre polynomials are derived, particularly first three ones? I was only given the table in the class, not steps to solving them......so I am curious.

2. Relevant equations
P0(x) = 1
P1(x) = x
P2(x) = 1/2 (3x2 - 1)

3. The attempt at a solution
......

2. Nov 12, 2014

### ShayanJ

One way is solving the Legendre equation($\frac{d}{dx} [(1-x^2) \frac{dP_n}{dx}]+n(n+1)P_n=0$) using the method of power series.(Substituting $y=\sum_{n=0}^\infty a_n x^n$ in the equation and finding a recursive relation for the coefficients.)

3. Nov 12, 2014

### terp.asessed

Thanks! The equation was NEVER given in the class, so I was stuck with the table, but again thanks!