File:LaguerreL60zeros.jpg
Plot of zeros of the LaguerreL polynomial of 60th order, being evaluated with naive Mathematica procedure,
ta60 = Table[ReplaceAll[x,Extract[NSolve[LaguerreL[60,x]==0, {x}, WorkingPrecision->60],n]], {n, 1, 60}]
lp60 = ListPlot[ta60, GridLines -> {{10, 20, 30, 40, 50, 60}, {50, 100, 150, 200}}]
Export["LaguerreL60zeros.jpg", lp60]
Description
Specification of the WorkingPrecision in the code above is important (at the default precision, the result would be wrong). The code seems to provide at least 16 correct decimal digits; they can be shown with code
N[TableForm[ta60], 16]
which gives the table below:
{
{0.02389797726272499},
{0.1259347188816908},
{0.3095789343267899},
{0.5749955420928053},
{0.9223694821166638},
{1.351938360008168},
{1.863996344299205},
{2.458895843822429},
{3.137049009785896},
{3.898929387204992},
{4.745073800125889},
{5.676084508246917},
{6.692631662786575},
{7.795456089031012},
{8.985372425657656},
{10.26327265503791},
{11.63013006384187},
{13.08700367935025},
{14.63504323401835},
{16.27549471920941},
{18.00970659885711},
{19.83913676543404},
{21.76536033437353},
{23.79007838949418},
{25.91512781160490},
{28.14249234607981},
{30.47431509373951},
{32.91291264408037},
{35.46079111232241},
{38.12066439392713},
{40.89547501481293},
{43.78841803594064},
{46.80296857185648},
{49.94291361031775},
{53.21238898258831},
{56.61592254269698},
{60.15848488450043},
{63.84554927953224},
{67.68316298705955},
{71.67803271444741},
{75.83762785465706},
{80.17030629260789},
{84.68546919450928},
{89.39375349025279},
{94.30727406611887},
{99.43993254288987},
{104.8078168074775},
{110.4297266865163},
{116.3278788975313},
{122.5288733841398},
{129.0650521852983},
{135.9764686041132},
{143.3138452602461},
{151.1432166956151},
{159.5536252388510},
{168.6708065489222},
{178.6839250131464},
{189.9052469621338},
{202.9339879504007},
{219.3181157737997}
}
This table can be included "as is" into the C++ code, in order to prepare, for example, the Gauss-Laguerre quadrature numerical implementation.
References
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:13, 1 December 2018 | | 360 × 226 (11 KB) | Maintenance script (talk | contribs) | Importing image file |
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