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arXiv · 1609.00829

Efficient computation of Laguerre polynomials

A. Gil·J. Segura·N. M. Temme
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Abstract

An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials $L^{(\alpha)}_n(z)$ are presented. The standard three-term recurrence relation satisfied by the polynomials and different types of asymptotic expansions valid for $n$ large and $\alpha$ small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter $\alpha$ and the degree $n$ satisfied by the polynomials, we claim that a relative accuracy close or better than $10^{-12}$ can be obtained using the module LaguerrePol for computing the functions $L^{(\alpha)}_n(z)$ in the parameter range $z \ge 0$, $-1 < \alpha \le 5$, $n \ge 0$.

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A. Gil, J. Segura, N. M. Temme. 2016-09-03. Efficient computation of Laguerre polynomials. https://doi.org/10.1016/j.cpc.2016.09.002

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