Efficient computation of Laguerre polynomials. An efficient algorithm and a Fortran 90 module (LaguerrePol) for computing Laguerre polynomials L(α)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 α small, are used depending on the parameter region. Based on tests of contiguous relations in the parameter α and the degree n satisfied by the polynomials, we claim that a relative accuracy close to or better than 10−12 can be obtained using the module LaguerrePol for computing the functions L(α)n(z) in the parameter range z≥0 , −1<α≤5 , n≥0 .
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References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Dunster, T. M.; Gil, A.; Segura, J.: Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions (2018)
- Terekhov, Andrew V.: The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver (2018)
- Gil, Amparo; Segura, Javier; Temme, Nico M.: Efficient computation of Laguerre polynomials (2017)