Questions tagged [laguerre-polynomials]

For questions about (associated) Laguerre polynomials, which arise in quantum physics.

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Convergence rate of Laguerre coefficients for polynomially bounded functions

Suppose $f:[0,\infty)\rightarrow\mathbb{R}$ satisfies: $$f(x)= \sum_{n=0}^\infty \hat{f}_n L_n(x),$$ for some $\hat{f}_0,\hat{f}_1,\dots\in\mathbb{R}$, where $L_n$ is the $n$th Laguerre polynomial for ...
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How to rearrange $py'' + (2l+2-2p)y' + 2(n-l-1)y = 0$ into $2py'' + (2l+2-2p)y' + (n-l-1)y = 0$?

I have a 2nd order homogenous ODE: $$py'' + (2l+2-2p)y' + 2(n-l-1)y = 0$$ where y is a function of p and n and l are variables Its solution is the associated Laguerre polynomials $L_{n-l-1}^{2l+1}(2p)$...
1 vote
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Find Special Function from Series Form?

I obtained this list of series (there are more but listed up to 5th order) and I suspect they are related to the Laguerre polynomials. Strictly speaking they are not $L_n^{\alpha}(x)$ but something ...
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Fractional Laguerre function $L_{n-\frac{1}{2}}(x)$

Is there any formula to represent Laguerre functions with fractional index (in this case only divided by 2) in terms of Bessel functions $I_0(x)$ and $I_1(x)$? I found this formula in Wolfram ...
1 vote
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Alternative roots of generalized Laguerre polynomials

$\require{\physics}$ Hi, I am wondering if it is possible to approximate the roots of the generalized Laguerre polynomial $L_n^{(\alpha)}(x)$ not with respect to $x$ but with respect to $n$, i.e. ...
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