# Legendre polynomial

1. Nov 22, 2005

### asdf1

can someone explain step-by-step why the legendre polynomial came into being? i'm having one hard time understanding it...

2. Nov 22, 2005

### mathphys

3. Nov 22, 2005

### Dr Transport

If memory serves me correctly, you can generate the Legendre polynomials using Gram-Schmidt orthogonalization on the interval $$-1 \leq x \leq 1$$ starting with a constant 1 as $$L_0$$.

The generating function method is used to calculate moments of charge distributions.

You have to master them to get anywhere in physics., they pop up all the time.

4. Nov 23, 2005

### rachmaninoff

Yup, assuming you start with the linearly independent set $$\{ 1, \, x, \, x^2, \, x^3 \ldots \}$$.

5. Nov 23, 2005

### asdf1

thank you very much!!! :)