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How to derive Legendre Polynomials?

  1. Nov 11, 2014 #1
    • 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. jcsd
  3. Nov 12, 2014 #2

    ShayanJ

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    Gold Member

    One way is solving the Legendre equation([itex]\frac{d}{dx} [(1-x^2) \frac{dP_n}{dx}]+n(n+1)P_n=0[/itex]) using the method of power series.(Substituting [itex] y=\sum_{n=0}^\infty a_n x^n [/itex] in the equation and finding a recursive relation for the coefficients.)
     
  4. Nov 12, 2014 #3
    Thanks! The equation was NEVER given in the class, so I was stuck with the table, but again thanks!
     
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