1. The problem statement, all variables and given/known data The Legendre polynomials [tex]P_l(x)[/tex] are a set of real polynomials orthogonal in the interval [tex]-1< x <1[/tex] , [tex] l\neq l' [/tex] [tex]\int dx P_l(x)P_l'(x)=0, -1<x<1[/tex] The polynomial [tex]P_l(x)[/tex] is of order l , that is, the highest power of x is [tex]x^l[/tex]. It is normalized to [tex]P_l(x)=1 [/tex] Starting with the set of functions , [tex] \varphi_l(x)=x^l, l=0,1,2,...,[/tex] used the orthogonalization procedure to derive the polynomials [tex] P_0,P_1,P_2, and P_3[/tex] 2. Relevant equations 3. The attempt at a solution I have no idea what my book (Peebles) means by orthogonalization procedure. But I looked at Griffifth book on QM , and perhaps they are talking about Rodrigues formula on p. 136 eqn. 4.28?