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Laguerre transform

  1. Jun 23, 2007 #1
    If we have the ODE introduced by Laguerre with n any Real number so

    x\,y'' + (1 - x)\,y' + n\,y = 0\,

    then i introduce the Laguerre transform (changing n from 0 to oo) in the form

    [tex] g(n)=\int_{0}^{\infty}dx\ f(x) L_{n} (x) [/tex]

    [tex] f(x)=\int_{0}^{\infty}dn\frac{ g(n)}{\Gamma (n+1)^{2}} L_{n} (x) [/tex]

    where in the last integral the variable is n and you integrate over all the possible positive index Laguerre function for x fixed, (although with a bit of inmodesty i call them Hoffmann-Laguerre transform )
  2. jcsd
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