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noblegas
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Homework Statement
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]