Rule: Q[1, 6, 52]

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.

Warning: This rule has negative weights!

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)
5.7099566690259474056 + 3.4669802398866029853e-2047j 8.31e-1006, 8.31e-1006j
1.9173533515278317401 + 2.094464702946029009e-2053j 8.72e-1012, 8.72e-1012j
6.7274828532751006587 - 1.27569405051844399e-2045j 1.5e-1004, 1.5e-1004j
0.38864472259608877018 - 8.8338049909790295596e-2058j 8.18e-1017, 8.18e-1017j
3.93413539189163899 + 3.5901274022258710558e-2050j 3.52e-1008, 3.52e-1008j
3.1748490704148367246 + 1.4500345364994254315e-2051j 2.12e-1009, 2.12e-1009j
4.779596384709730006 + 4.4272455322296491574e-2048j 5.08e-1007, 5.08e-1007j
0.18796958875044643007 + 1.7543047495213915115e-2061j 3.92e-1018, 3.92e-1018j
1.4176754723070136151 - 7.5253491193787858549e-2054j 5.29e-1013, 5.29e-1013j
1 - 2.7634767594022621369e-2055j 3.26e-1014, 3.26e-1014j
0.65872941300383190841 + 1.282556392564653188e-2056j 1.72e-1015, 1.72e-1015j
2.5026000900489822054 + 1.2183114560361251934e-2052j 1.35e-1010, 1.35e-1010j
0.058342862707844573428 + 5.4069106181433566109e-2061j 9.37e-1020, 9.37e-1020j
0.002465169367667945629 - 2.7473319293773505507e-2062j 9.04e-1022, 9.04e-1022j
202.21050402552422767 - 1.9399065547248240082e-2036j 2.87e-1002, 2.87e-1002j
173.65599040178298181 - 7.518474107704072045e-2034j 3.94e-999, 3.94e-999j
153.10973181466640312 - 5.9902793285537603625e-2066j 3.98e-997, 3.98e-997j
144.30919618374005992 - 1.9579093454696271403e-2101j 2.34e-996, 2.34e-996j
186.29225559057427563 + 2.3076685992000923001e-2116j 1.67e-1000, 1.67e-1000j
40.44723755352699538 + 5.5312513753263490675e-2129j 1.58e-994, 1.58e-994j
108.73726415625262202 - 1.26139387669045759e-2147j 7.32e-994, 7.32e-994j
15.480725837411339234 + 5.4619858185263103399e-2165j 9.84e-1000, 9.84e-1000j
43.445072981501720068 + 2.4684718168644367771e-2157j 3.11e-994, 3.11e-994j
64.46494873076832243 + 2.4162192549969983163e-2156j 5.17e-993, 5.17e-993j
60.571097055653037539 - 2.3814883492220856753e-2177j 3.85e-993, 3.85e-993j
72.781642898995312262 - 1.291543888348936934e-2230j 6.54e-993, 6.54e-993j
86.736141169298115674 - 3.6117525019468978648e-2286j 5.34e-993, 5.34e-993j
13.901584578154500143 + 2.7889399496004621753e-2328j 2.62e-1000, 2.62e-1000j
9.9025645160048522366 - 8.1186769431372622676e-2330j 5.96e-1002, 5.96e-1002j
8.2300947527492967703 - 1.0927312478240237923e-2329j 5.18e-1002, 5.18e-1002j
37.580704821233417713 - 2.8884404691179274279e-2321j 6.68e-995, 6.68e-995j
102.81190228741326124 + 1.0992982376178739988e-2348j 1.46e-993, 1.46e-993j
162.7902722350950318 - 4.469660031607012287e-2383j 4.61e-998, 4.61e-998j
53.271621574327692156 - 4.0271236941278498104e-2430j 1.89e-993, 1.89e-993j
18.989963815544515587 + 9.1597824860510589719e-2468j 1.15e-998, 1.15e-998j
91.835208765727038599 - 8.0804714611081056803e-2485j 3.73e-993, 3.73e-993j
25.095082345147903429 + 3.7403693948318043019e-2512j 4.58e-997, 4.58e-997j
27.355755165185527387 - 1.5007851830226665604e-2509j 1.41e-996, 1.41e-996j
49.852264490684589194 - 1.1041976174403071285e-2529j 1.16e-993, 1.16e-993j
114.99427565207405147 - 1.1150187421825892402e-2583j 3.64e-994, 3.64e-994j
97.186555183277550272 - 4.9767821392684165964e-2638j 2.59e-993, 2.59e-993j
11.124699782802479565 - 1.5311165095265203301e-2668j 1.78e-1001, 1.78e-1001j
22.948079594501460522 - 1.48223597923962717e-2663j 1.47e-997, 1.47e-997j
32.226432223302262539 - 8.1899638087644976091e-2661j 1.11e-995, 1.11e-995j
34.841600169195188114 + 1.4967696824520603291e-2680j 2.81e-995, 2.81e-995j
17.17842709632752695 + 7.8613377885789067566e-2711j 3.52e-999, 3.52e-999j
8.5922441271970337409 + 7.4020659239167491087e-2720j 4.78e-1002, 4.78e-1002j
136.20373826781338386 - 3.8968817618239372342e-2776j 1.15e-995, 1.15e-995j
128.67040756110497636 - 4.0463755439533052902e-2874j 4.26e-995, 4.26e-995j
7.9886543552868417152 + 7.216122287657680523e-2931j 2.12e-1002, 2.12e-1002j
121.62211747826395275 + 5.2933728238487422444e-2941j 1.28e-994, 1.28e-994j
81.870977895150555586 + 1.7630085773734128865e-2976j 6.12e-993, 6.12e-993j
29.732073459119772966 + 1.2268392169703459756e-3000j 4.01e-996, 4.01e-996j
12.448513062956781353 + 2.8418192344810660356e-3006j 6.11e-1001, 6.11e-1001j
68.532080441448810035 + 2.3332017227800512118e-2996j 6.18e-993, 6.18e-993j
77.224002543990175111 + 1.1484812495032469719e-3010j 7.19e-993, 7.19e-993j
56.842402904834913972 + 1.6800644148776508305e-3017j 2.76e-993, 2.76e-993j
46.578500119235044865 - 1.4539955298213692039e-3022j 6.53e-994, 6.53e-994j
20.91328935581141055 - 1.9279381813798144854e-3035j 4.29e-998, 4.29e-998j

Weights

Weight (ball center) Error (ball radius)
0.0032222170677237133733 - 1.5612206823602237786e-2048j 2.8e-69, 8.63e-823j
0.079681703684121110314 + 1.1023604926314358165e-2048j 8.83e-43, 2.73e-796j
0.001278221215984687496 - 3.9256303538363763408e-2049j 1.16e-73, 3.57e-827j
0.15961972426994769442 + 1.4117839848162672079e-2048j 8.1e-35, 2.5e-788j
0.015700503724588720428 - 8.3697648508786058489e-2049j 8.52e-61, 2.63e-814j
0.02992271270547198438 + 8.6332922820390730547e-2049j 5e-56, 1.54e-809j
0.0074595162170721880879 + 1.0405151237618855506e-2048j 1.53e-65, 4.71e-819j
0.13721410177377374324 - 1.2287968345955723383e-2048j 5.07e-35, 1.56e-788j
0.11093290980574304333 - 1.2690032004108345916e-2048j 2.5e-39, 7.73e-793j
0.13922412814943559833 + 1.4118645742424978639e-2048j 4.84e-37, 1.49e-790j
0.15785328956146184518 - 1.4724474879626417549e-2048j 7.03e-36, 2.17e-789j
0.051468625510642831562 - 9.5810628245949538897e-2049j 3.71e-51, 1.15e-804j
0.087920650588475932625 + 9.2902034707682381272e-2049j 1.49e-35, 4.6e-789j
0.017842564568248624566 - 3.7460780450963504689e-2049j 7.89e-36, 2.43e-789j
2.853660221357400299e-87 + 7.6374329947448575633e-2098j 5.85e-163, 1.81e-916j
4.4377509053035718735e-75 + 1.7886305066762761334e-2091j 2.3e-159, 7.1e-913j
2.9457405276945317318e-66 + 7.7825308564525275542e-2087j 9.36e-157, 2.89e-910j
1.7908712194563674594e-62 - 7.7708423930978658402e-2085j 1.2e-155, 3.7e-909j
1.723330671314179021e-80 - 2.6342592805147519184e-2094j 1.55e-161, 4.8e-915j
7.9630338431715031266e-18 + 4.4257166666076178352e-2060j 6.65e-129, 2.05e-882j
3.6332278582120602747e-47 + 1.1536991385469260117e-2076j 7.52e-151, 2.32e-904j
3.1010753998182108824e-07 - 1.9078881172254863757e-2052j 1.76e-108, 5.43e-862j
4.1539188893859553994e-19 - 7.204006702747552809e-2061j 9.23e-131, 2.85e-884j
4.008747849776261121e-28 - 3.6972612353631104639e-2066j 2.57e-140, 7.94e-894j
1.8846529833495531582e-26 + 3.3469944905888806696e-2065j 4.71e-139, 1.45e-892j
1.0696360506817804156e-31 - 3.5349202398447808133e-2068j 1.38e-143, 4.25e-897j
1.0669407183715576993e-37 + 1.6458305604638102514e-2071j 6.46e-148, 2e-901j
1.3923222283220559359e-06 + 8.9261351271836869329e-2052j 4.89e-112, 1.51e-865j
5.9881510794136025835e-05 - 1.0799195580616788661e-2049j 8.32e-106, 2.57e-859j
-0.00086205455563989676222 - 9.766538950031154454e-2048j 4.01e-102, 1.24e-855j
1.337849572688401427e-16 - 2.5828307028164230266e-2059j 1.5e-131, 4.64e-885j
1.2899691911003354986e-44 - 2.7593735089071152929e-2075j 3.01e-152, 9.29e-906j
2.0417033896949588933e-70 - 5.018441162496792815e-2089j 9.12e-163, 2.82e-916j
2.5571562471573503359e-23 + 2.200997225443565377e-2063j 2.9e-139, 8.94e-893j
1.0569333224799254998e-08 - 9.1106894134353010829e-2054j 1.15e-122, 3.55e-876j
6.8281568471853852992e-40 - 1.0294020757341850485e-2072j 4.92e-150, 1.52e-903j
2.782701257065348448e-11 + 9.2895897664394026586e-2056j 3.03e-128, 9.35e-882j
3.0526999055683041719e-12 - 1.9369479023982020401e-2056j 1.06e-129, 3.26e-883j
7.4802434200187167581e-22 - 1.6125160592467687024e-2062j 8.66e-139, 2.67e-892j
7.3651045297167485974e-50 - 4.0971743051701255165e-2078j 2.35e-156, 7.27e-910j
3.4005168223388878196e-42 + 5.697650726410860829e-2074j 9.15e-152, 2.83e-905j
1.8633194886798807928e-05 + 2.0430170742877057343e-2050j 2.54e-119, 7.85e-873j
2.2597908787719068259e-10 - 4.3482421961202059236e-2055j 4.01e-129, 1.24e-882j
2.5793212624889195519e-14 - 7.6551476579527845845e-2058j 3.13e-134, 9.67e-888j
1.9772717943443892285e-15 + 1.43722973275624879e-2058j 4.3e-135, 1.33e-888j
6.0787992099308289404e-08 + 4.1492314485052187788e-2053j 1.5e-126, 4.63e-880j
0.00042518159648657327399 + 2.8850745202383158787e-2048j 5.05e-119, 1.56e-872j
5.4916210286135233528e-59 + 5.4822812816695156948e-2083j 1.43e-162, 4.4e-916j
9.5762018939726887802e-56 - 2.9075255295500101117e-2081j 1.88e-161, 5.81e-915j
0.0010102690637099599475 + 8.3073848531308459648e-2048j 3.01e-122, 9.29e-876j
1.0340126478666649014e-52 + 1.2113956871272198743e-2079j 4.81e-160, 1.48e-913j
1.3210299656362572452e-35 - 2.3511578087652561618e-2070j 8.8e-153, 2.72e-906j
2.9785644042785842041e-13 + 3.918920125918395725e-2057j 2.48e-138, 7.67e-892j
5.4446662733715121854e-06 - 4.2464244431140303607e-2051j 1.9e-130, 5.86e-884j
7.172114236447467839e-30 + 3.7717408262616791305e-2067j 2.9e-150, 8.94e-904j
1.3162633165580222257e-33 + 3.0261619409834596322e-2069j 3.29e-152, 1.02e-905j
7.5124910957710232348e-25 - 2.8114594133995794133e-2064j 7.69e-148, 2.37e-901j
1.8912084698580771033e-20 + 1.1098876380667608474e-2061j 2.27e-145, 6.99e-899j
1.6365191424118664912e-09 + 1.9999021124099581793e-2054j 3.16e-138, 9.76e-892j

Download

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