Rule: Q[1, 100]

Type

This rule is of Laguerre type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
341.37260337471421063 + 7.2885327158831611636e-4773j 5.89e-2007, 5.89e-2007j
315.21603775532268274 - 1.3739917562856010028e-4767j 4.12e-2004, 4.12e-2004j
303.84915630172523675 - 1.2696909381104862265e-4766j 5.97e-2003, 5.97e-2003j
327.60231574730985787 + 3.6171496705989216854e-4770j 1.96e-2005, 1.96e-2005j
265.10692901837606991 + 5.3875622108419086125e-4774j 2.8e-1999, 2.8e-1999j
274.00014471504054717 + 2.9913875448947462361e-4818j 4.37e-2000, 4.37e-2000j
145.53702701671588207 + 7.8608205363761381942e-4914j 1.36e-1992, 1.36e-1992j
119.26340195142187167 + 8.7243649493965082938e-5078j 1.03e-1992, 1.03e-1992j
160.23553842881068529 + 1.3418660479952519269e-5248j 7.71e-1993, 7.71e-1993j
31.209418095739951863 + 5.0009357378581487152e-5338j 3.28e-2005, 3.28e-2005j
22.833238771896448915 + 4.6080119553127201403e-5351j 5.56e-2009, 5.56e-2009j
165.396403017355116 - 1.5144352778572881429e-5357j 5.12e-1993, 5.12e-1993j
49.956429986235564112 + 4.6179018184434758372e-5413j 1e-1999, 1e-1999j
26.015780623429754442 + 5.965341875050653812e-5426j 1.93e-2007, 1.93e-2007j
76.885144316034859123 + 3.6133680962395579237e-5411j 2.29e-1995, 2.29e-1995j
47.629215878727493745 + 1.02079322779541905e-5441j 3.12e-2000, 3.12e-2000j
21.324506473975389939 - 1.7322096731341401931e-5484j 8.73e-2010, 8.73e-2010j
65.287329297043545119 + 8.4896652137805015617e-5477j 7.26e-1997, 7.26e-1997j
219.08632604341690956 - 1.0492313684571246369e-5568j 1.08e-1995, 1.08e-1995j
54.802542862699800187 - 3.1571622202873896874e-5622j 1.06e-1998, 1.06e-1998j
33.054648080184242895 - 1.3929777479360119588e-5658j 1.48e-2004, 1.48e-2004j
357.22824452456994679 - 2.1689588207598645895e-5699j 9.99e-2009, 9.99e-2009j
17.123338742268485523 - 9.552422980559817263e-5772j 2.89e-2012, 2.89e-2012j
18.46995829563585631 - 4.0030188900495535044e-5775j 2.01e-2011, 2.01e-2011j
181.74573987575728158 - 1.0900122765953767132e-5842j 1.36e-1993, 1.36e-1993j
199.55318147190641264 - 6.7274634214071729621e-5953j 1.66e-1994, 1.66e-1994j
27.690518399545598562 + 9.0498786944231903044e-6009j 1.18e-2006, 1.18e-2006j
34.957819192560012625 + 1.013458418809174456e-6005j 7.15e-2004, 7.15e-2004j
96.550074651380524101 - 5.560494091319889781e-5994j 1.09e-1993, 1.09e-1993j
226.04313985490743259 - 2.6125957790373675159e-6038j 3.79e-1996, 3.79e-1996j
59.910233420605013684 - 5.1789088235980321375e-6071j 9.93e-1998, 9.93e-1998j
89.676565136756757901 - 3.4993281615753423419e-6066j 3.75e-1994, 3.75e-1994j
68.07956614124264243 - 1.0933648811618649876e-6078j 1.76e-1996, 1.76e-1996j
240.73417881278629322 - 1.7849500556963921835e-6093j 2.91e-1997, 2.91e-1997j
11.182398650431342872 - 1.9433130157159698194e-6152j 7.81e-2017, 7.81e-2017j
248.51584885440904927 + 2.3344440925834375489e-6127j 6.86e-1998, 6.86e-1998j
43.162330079860613822 + 5.3773525808107994287e-6156j 2.09e-2001, 2.09e-2001j
7.3617517918770738554 - 1.1307383811823537809e-6176j 8.05e-2021, 8.05e-2021j
73.877221882054578435 + 1.9847408544936958525e-6147j 1.04e-1995, 1.04e-1995j
52.347249698815751892 - 4.1713456177417609436e-6156j 3.32e-1999, 3.32e-1999j
131.9148046078552246 + 7.2143057904330374925e-6147j 1.5e-1992, 1.5e-1992j
123.37825236725466785 + 5.6447347726799119449e-6166j 1.24e-1992, 1.24e-1992j
376.98630496913472066 - 2.2294991190659742882e-6195j 5.11e-2011, 5.11e-2011j
293.28124643006866447 + 1.0722027666007785175e-6179j 6.77e-2002, 6.77e-2002j
19.870216867244689907 - 2.1571688614827257923e-6207j 1.38e-2010, 1.38e-2010j
15.829985154632621758 + 5.503272908144245346e-6210j 3.83e-2013, 3.83e-2013j
1.7114730319872570149 + 1.0929672422908905412e-6227j 7.52e-2031, 7.52e-2031j
86.361742365815246608 + 1.8691841033994957606e-6188j 2.06e-1994, 2.06e-1994j
2.1407673083407700572 - 1.7995596661674347507e-6235j 1.09e-2029, 1.09e-2029j
2.619320053779712601 + 4.0556643759724140684e-6235j 1.61e-2028, 1.61e-2028j
212.36278335242995751 + 6.1442064810427091006e-6198j 2.85e-1995, 2.85e-1995j
115.24689222727119132 - 2.2802260026989266691e-6210j 7.58e-1993, 7.58e-1993j
9.1697949418617843112 - 3.3062300548718682035e-6253j 9.27e-2019, 9.27e-2019j
3.7248093495769746578 + 8.0757753230570337288e-6261j 3.15e-2026, 3.15e-2026j
283.36604976768235436 + 3.8900201946642064918e-6228j 6.09e-2001, 6.09e-2001j
155.20886000440045295 + 2.0977914537812128912e-6255j 1e-1992, 1e-1992j
187.50816980671865161 - 9.1199943701627398738e-6294j 6.92e-1994, 6.92e-1994j
93.072085147080409323 + 9.350917256469882671e-6313j 6.44e-1994, 6.44e-1994j
233.25184161809797726 - 2.0648710418945947425e-6327j 1.09e-1996, 1.09e-1996j
1.3312778504405214702 + 8.4445291602024702116e-6399j 3.91e-2032, 3.91e-2032j
103.76108096995971452 - 3.9925362147893088334e-6359j 2.68e-1993, 2.68e-1993j
5.7563920881198243408 + 8.1259563703442756736e-6448j 7.06e-2023, 7.06e-2023j
127.59434901906862632 - 3.6144107548897313685e-6414j 1.4e-1992, 1.4e-1992j
36.919530638842257776 + 7.071267135453554725e-6473j 3.16e-2003, 3.16e-2003j
13.401674719803223181 + 7.2876640614100524604e-6498j 5.93e-2015, 5.93e-2015j
6.5338450957947748674 + 3.0064486017423243168e-6504j 7.66e-2022, 7.66e-2022j
170.69732328953824988 - 4.4481147449794357636e-6474j 3.62e-1993, 3.62e-1993j
14.589542810336053197 + 9.2815891858818976446e-6524j 4.85e-2014, 4.85e-2014j
8.2403259338539284779 - 1.121041976951135751e-6529j 8.76e-2020, 8.76e-2020j
79.967575981307061382 + 3.5937932146137940705e-6502j 5.01e-1995, 5.01e-1995j
1 + 4.2738675183408242211e-6568j 2.08e-2033, 2.08e-2033j
3.1472831741094566083 - 1.1636188407509561014e-6561j 2.15e-2027, 2.15e-2027j
12.266061062185372412 + 1.0002984021645563703e-6550j 6.96e-2016, 6.96e-2016j
193.44074085053836983 - 4.2133324070826723692e-6527j 3.6e-1994, 3.6e-1994j
5.0291920873566517764 + 9.0949400080494599572e-6586j 4.98e-2024, 4.98e-2024j
41.021113685021340001 - 9.4132623062083495391e-6564j 5.75e-2002, 5.75e-2002j
0.71740733942500269294 + 5.6653012693276956531e-6597j 9.93e-2035, 9.93e-2035j
70.942457033138417526 + 1.3939193236253465939e-6554j 4.34e-1996, 4.34e-1996j
10.150400420892620701 + 1.8620465898240887104e-6591j 8.75e-2018, 8.75e-2018j
136.34296024415192779 - 3.4360358240632649725e-6564j 1.59e-1992, 1.59e-1992j
205.85641516348669822 - 1.0250093810457170614e-6601j 7.42e-1995, 7.42e-1995j
4.3520567860206314003 + 3.6821453848448025436e-6670j 3.89e-2025, 3.89e-2025j
62.564586374215173382 - 4.9940475471198482904e-6638j 2.76e-1997, 2.76e-1997j
256.62762312393833052 - 6.8720381994146765499e-6639j 1.53e-1998, 1.53e-1998j
150.31099863974642701 + 1.2596804505286249854e-6672j 1.27e-1992, 1.27e-1992j
45.364779337000350143 - 2.0481121351074871323e-6724j 7.93e-2001, 7.93e-2001j
24.39684577526474659 - 8.0016823992859792679e-6732j 3.53e-2008, 3.53e-2008j
29.421557005244975256 - 3.2290012449323603557e-6730j 5.8e-2006, 5.8e-2006j
176.14473846138540907 - 5.0722475544336991809e-6716j 2.28e-1993, 2.28e-1993j
38.940409826749917579 + 6.5985909846230235897e-6759j 1.35e-2002, 1.35e-2002j
140.88240967508372427 - 8.2082667679539297396e-6748j 1.47e-1992, 1.47e-1992j
100.11241017990650853 + 3.8431270145685938716e-6760j 1.8e-1993, 1.8e-1993j
0.15716766964257947573 - 9.6330582410875805018e-6807j 9.47e-2039, 9.47e-2039j
0.062936498456763708476 + 8.8905156153926091926e-6808j 3.05e-2040, 3.05e-2040j
111.32600609053927811 + 1.1793467493159552297e-6759j 5.69e-1993, 5.69e-1993j
83.125941247410460189 - 1.0740116181893908216e-6764j 9.81e-1995, 9.81e-1995j
0.011809067607446053697 - 6.4963572323328174655e-6897j 1.28e-2041, 1.28e-2041j
0.29672649978832526904 + 2.7946047607386765958e-6808j 2.72e-2037, 2.72e-2037j
0.48316366208964027978 - 7.3935259706468463341e-6806j 5.87e-2036, 5.87e-2036j
107.49819833325647606 - 1.2992105388322929548e-6761j 4.09e-1993, 4.09e-1993j
57.323219343842241757 + 5.103267840745287438e-6769j 3.23e-1998, 3.23e-1998j

Weights

Weight (ball center) Error (ball radius)
8.1204105942287421264e-148 - 1.2726711928650567458e-4906j 3.47e-351, 2.55e-1853j
1.5012160414044402615e-136 - 5.7621574466691122557e-4901j 4.72e-348, 3.46e-1850j
1.1993244998311380901e-131 + 1.1456281426198939441e-4897j 7.3e-347, 5.36e-1849j
6.8873012522046931128e-142 + 1.3199219257808878366e-4903j 7.21e-350, 5.29e-1852j
6.3668575473149164078e-115 - 1.7060328140142551596e-4888j 7.53e-343, 5.53e-1845j
9.1869778294917115152e-119 - 4.7744380197242839372e-4891j 6.33e-344, 4.65e-1846j
2.9337433710815682265e-63 + 1.7962524658839622133e-4864j 1.33e-321, 9.75e-1824j
6.5109723223435130014e-52 + 6.9095482462571045582e-4859j 2.22e-314, 1.63e-1816j
1.3108398574367699869e-69 - 1.3728872421032259609e-4867j 1.22e-325, 8.93e-1828j
5.0716111542405340552e-14 - 3.7622673548136013497e-4840j 2.32e-264, 1.7e-1766j
1.8623818536695700479e-10 + 2.1966903747709837448e-4838j 1.91e-252, 1.4e-1754j
7.722282249281148078e-72 + 1.1095377418013769006e-4868j 4.67e-327, 3.43e-1829j
4.7522925736549831595e-22 + 3.9700348291129777267e-4844j 2.44e-283, 1.79e-1785j
8.2816923311010995993e-12 + 4.6979905701972221038e-4839j 1.95e-258, 1.43e-1760j
1.2381853496367810956e-33 + 7.3464967309210575784e-4850j 1.95e-300, 1.43e-1802j
4.74032053603848329e-21 - 1.2400866445275990412e-4843j 8.74e-282, 6.42e-1784j
8.1202382652773207615e-10 - 4.556322431693148966e-4838j 8.68e-253, 6.37e-1755j
1.2205550661796626611e-28 + 2.1700291502099650563e-4847j 1.93e-294, 1.41e-1796j
4.8629786845634164544e-95 - 6.15185021620883637e-4880j 2.94e-341, 2.16e-1843j
3.9389336398488879187e-24 + 3.6997261227818082614e-4845j 5.95e-288, 4.36e-1790j
8.2668905152544396576e-15 + 1.5315619059774475701e-4840j 5.15e-270, 3.78e-1772j
1.2479581977941198509e-154 + 4.2939027255827605637e-4910j 1.14e-361, 8.35e-1864j
4.8303437407574073766e-08 + 3.4487491193783968023e-4837j 6.37e-250, 4.67e-1752j
1.3073391672422400313e-08 - 1.8050898505332586635e-4837j 5.69e-252, 4.17e-1754j
6.6558332036237521183e-79 - 3.9126431837672181834e-4872j 3.35e-334, 2.45e-1836j
1.3426403099688990154e-86 + 7.1092053046866443041e-4876j 4.42e-338, 3.24e-1840j
1.6044460966266444622e-12 - 2.0832372327155238675e-4839j 1.09e-266, 7.97e-1769j
1.2708531446588248495e-15 - 6.0566014176625758627e-4841j 6.86e-275, 5.04e-1777j
4.1243769967973930934e-42 + 4.7448627434275780018e-4854j 4.46e-313, 3.28e-1815j
4.7941233835044442081e-98 + 2.2856620626899107204e-4881j 2.66e-343, 1.95e-1845j
2.5101661286609490426e-26 + 3.0286904913612435799e-4846j 2.73e-295, 2e-1797j
3.7987451077231471426e-39 + 1.382518929328116511e-4852j 9.88e-311, 7.25e-1813j
7.6701184883498643017e-30 - 5.5185892373879122006e-4848j 4.32e-300, 3.17e-1802j
2.1520270930245567159e-104 + 2.4851782503649544428e-4884j 9.8e-347, 7.19e-1849j
1.4721188757195947041e-05 - 5.8548346691708841474e-4836j 3.28e-253, 2.41e-1755j
9.3501571331093879611e-108 - 7.679851412032539664e-4886j 4.43e-348, 3.25e-1850j
3.9051709387290377579e-19 - 1.1022770114597174068e-4842j 5.29e-288, 3.88e-1790j
0.00054185680980998091887 - 3.4783835103773789833e-4835j 2.85e-245, 2.09e-1747j
2.4459693057296421959e-32 - 3.2128425994898193498e-4849j 6.87e-305, 5.04e-1807j
4.4690509261627588937e-23 - 1.2314736884355595384e-4844j 5.08e-293, 3.73e-1795j
2.2437791340531973751e-57 - 1.4070706689483225702e-4861j 5.6e-327, 4.11e-1829j
1.0892259178165574695e-53 - 9.2015700918667931876e-4860j 1.83e-324, 1.35e-1826j
4.3917994600987456711e-163 - 2.1484859780439985543e-4914j 6.85e-372, 5.03e-1874j
4.3559761386710948471e-127 - 1.2816388870300595645e-4895j 1.92e-357, 1.41e-1859j
3.3493572276205081705e-09 + 9.1939611835005823968e-4838j 2.97e-274, 2.18e-1776j
1.6898442714099739468e-07 - 6.4127265847056267428e-4837j 9.55e-271, 7.01e-1773j
0.07309170694595776547 + 3.7472872111607679519e-4834j 2.88e-226, 2.11e-1728j
1.0204424154582383626e-37 - 7.0300436324563051829e-4852j 5.33e-314, 3.91e-1816j
0.053362328188224512563 - 3.250301750481833867e-4834j 6.84e-232, 5.02e-1734j
0.036661704519272038052 + 2.7261047478378239159e-4834j 1.7e-236, 1.24e-1738j
3.9118115332194279294e-92 + 1.5168108105606482765e-4878j 1.31e-344, 9.63e-1847j
3.5278552713086797432e-50 - 4.9471042791791552698e-4858j 2.41e-324, 1.77e-1826j
9.9451217482585233065e-05 - 1.5059070780402006727e-4835j 7.64e-266, 5.61e-1768j
0.014527532072739467589 + 1.746916703004524099e-4834j 5.54e-249, 4.07e-1751j
8.3010108165033806023e-123 + 2.3406637540052959268e-4893j 2.91e-356, 2.14e-1858j
1.9464981500761547608e-67 + 1.5947943598855333813e-4866j 2.46e-334, 1.81e-1836j
2.1532430561450190569e-81 + 2.3948795932453146485e-4873j 4.94e-341, 3.63e-1843j
1.304419107581620259e-40 - 2.6134365411310191847e-4853j 4.62e-319, 3.39e-1821j
3.6796189734898412681e-101 - 7.8079201646046932561e-4883j 1.43e-348, 1.05e-1850j
0.093955287697652861969 - 4.1648535567143155732e-4834j 8.6e-244, 6.31e-1746j
3.1949150060030233162e-45 + 1.3807950288728017188e-4855j 2.14e-323, 1.57e-1825j
0.0023791309382103231176 - 7.208797335595476582e-4835j 8.32e-270, 6.11e-1772j
1.6469338522516599087e-55 + 1.1668612357604097194e-4860j 1.03e-328, 7.53e-1831j
1.8414668638567531726e-16 + 2.3260411393832684856e-4841j 6.51e-300, 4.78e-1802j
1.7571809580097029914e-06 - 2.0446996179882503752e-4836j 7.68e-284, 5.64e-1786j
0.0011665700326771486541 + 5.0762849019938963762e-4835j 9.1e-274, 6.68e-1776j
3.9565326106934357865e-74 - 8.3983816379281395033e-4870j 1.85e-338, 1.36e-1840j
5.5988225418673846487e-07 + 1.1606106333590416154e-4836j 4.16e-285, 3.05e-1787j
0.0002384690073914581243 + 2.319755015694151733e-4835j 4.11e-278, 3.02e-1780j
5.8170012326620992688e-35 - 1.6193857567846477359e-4850j 5.21e-317, 3.82e-1819j
0.11289862668209834882 + 4.4413036393713525309e-4834j 7.36e-260, 5.4e-1762j
0.023749614702423955963 - 2.2154200320166197536e-4834j 2.23e-268, 1.63e-1770j
5.2249177155167342569e-06 + 3.5067068272817656713e-4836j 7.97e-284, 5.85e-1786j
5.8804052658479386767e-84 - 1.3578201312119468834e-4874j 6.24e-343, 4.58e-1845j
0.0045948532587538616239 + 9.9588429488341491665e-4835j 6.42e-276, 4.71e-1778j
3.2300748230889691155e-18 + 3.1389230775852346194e-4842j 2.68e-304, 1.96e-1806j
0.12607863292649367998 - 4.5090234812544837006e-4834j 5.04e-266, 3.7e-1768j
4.490281511348178329e-31 + 1.3553513521876627663e-4848j 1.9e-314, 1.4e-1816j
3.9304874017518172138e-05 + 9.5166154098317495356e-4836j 9.01e-285, 6.61e-1787j
2.7453075980561581513e-59 + 1.6110407519167074494e-4862j 3.31e-332, 2.43e-1834j
2.5354326576901748553e-89 - 3.4269959180090275262e-4877j 1.1e-345, 8.06e-1848j
0.0084000481239876230916 - 1.3378893907165029229e-4834j 8.65e-282, 6.35e-1784j
1.8114825975962189524e-27 - 8.2451743820818439968e-4847j 1.23e-313, 9.03e-1816j
2.9276763688641878783e-111 + 2.6927830802501143133e-4887j 6.3e-356, 4.62e-1858j
2.5419723866678966106e-65 - 1.7430720501500474034e-4865j 1.94e-335, 1.42e-1837j
4.4389115904951597665e-20 + 3.7546090815254734643e-4843j 1.71e-309, 1.26e-1811j
4.0393131914599342487e-11 - 1.0301348856598791901e-4838j 8.63e-302, 6.33e-1804j
2.9358581889842589809e-13 + 8.9801467669492316731e-4840j 4.51e-304, 3.31e-1806j
1.7518001203228738271e-76 + 5.9387514086393387534e-4871j 8.65e-341, 6.35e-1843j
2.5135798160732738067e-17 - 8.6731646456834343402e-4842j 2.07e-308, 1.52e-1810j
3.0058076379085720132e-61 - 1.7486474483542770295e-4863j 4.12e-334, 3.02e-1836j
1.1985535610785600257e-43 - 8.2666396990232304564e-4855j 7.47e-327, 5.48e-1829j
0.099619939547572266149 + 2.8668033830060384215e-4834j 2.79e-299, 2.05e-1801j
0.06786049745409654489 - 1.7015773315771101706e-4834j 1.71e-299, 1.26e-1801j
1.7373300785555331517e-48 + 3.3814334385749978383e-4857j 8.82e-330, 6.47e-1832j
2.532686404539518045e-36 + 3.4388316414712049141e-4851j 1.16e-323, 8.53e-1826j
0.030038781858926169055 + 5.3453097229300670043e-4835j 2.75e-302, 2.02e-1804j
0.12100010133913803599 - 3.7591290399538517646e-4834j 2.14e-302, 1.57e-1804j
0.12967306387388016198 + 4.3003806334784531725e-4834j 1.61e-302, 1.18e-1804j
7.7957160903620564977e-47 - 2.2090329611147137979e-4856j 4.38e-329, 3.21e-1831j
3.2509406299887573332e-25 - 1.076078252023265902e-4845j 5.25e-318, 3.85e-1820j

Download

All rules of Laguerre type can be downloaded here packed into a single file.