The Laguerre polynomials,(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right)

[/itex]

have [itex] n [/itex] real, strictly positive roots in the interval [itex] \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] [/itex]

I am interested in a closed form expression of these roots, that is, I would like to avoid any method of finding these roots, such as, Laguerre's method.

Any ideas are most welcome.

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# Closed form expression of the roots of Laguerre polynomials

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