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Legendre second kind

  1. Sep 19, 2015 #1
    Legendre functions $Q_n(x)$ of the second kind
    \begin{equation*}
    Q_n(x)=P_n(x) \int \frac{1}{(1-x^2)\cdot P_n^2(x)}\, \mathrm{d}x
    \end{equation*}
    what to do after this step?
    how can I complete ?
    I need to reach this formula
    \begin{equation*}
    Q_n(x)=\frac{1}{2} P_n(x)\ln\left( \frac{ 1+x}{1-x}\right)
    \end{equation*}
     
  2. jcsd
  3. Sep 19, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    If that were true then, setting the two forms for [itex]Q_(x)[/itex] equal, it would have to be true that
    [tex]\int \frac{1}{(1- x^2)P^2_n(x)}dx= \frac{1}{2}ln\left(\frac{1+ x}{1- x}\right)[/tex]

    Is that true? I suggest you check your formulas.
     
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