If we have the ODE introduced by Laguerre with n any Real number so(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

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

[/tex]

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 )

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# Laguerre transform

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