Rule: Q[4, 5, 22, 42]

Type

This rule is of Hermite (probabilists') 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)
10.116322201480710748 + 2.6948244489043786042e-1097j 1.64e-494, 1.64e-494j
-11.234428620241886258 - 4.2449164299031139067e-1107j 1.35e-495, 1.35e-495j
11.234428620241886258 - 1.0330209204394818897e-1104j 1.37e-495, 1.37e-495j
-8.085235231949366002 - 1.3153554012261644784e-1112j 1.09e-493, 1.09e-493j
-5.3351793308275412103 + 4.3777795148442224799e-1114j 2.95e-495, 2.95e-495j
14.162057069963751664 + 3.0665078705726517032e-1115j 1.79e-499, 1.79e-499j
11.847350534644544078 + 8.4626922808215175651e-1112j 2.99e-496, 2.99e-496j
-11.847350534644544078 + 9.019695015466759509e-1122j 3.29e-496, 3.29e-496j
-13.259521897775622893 - 6.8770983336612158269e-1123j 4.63e-498, 4.63e-498j
2.3344142183389772393 - 9.7902381608144119912e-1125j 6.09e-501, 6.09e-501j
4.6962899838364346202 + 3.6428578604875673152e-1118j 5.53e-496, 5.53e-496j
-9.1301035544069820442 + 1.4175479305087914041e-1126j 1.35e-493, 1.35e-493j
-12.512929139450520771 - 6.3172960220330963976e-1132j 4.76e-497, 4.76e-497j
-6.80585310157933011 - 7.5812849589701064468e-1130j 3.7e-494, 3.7e-494j
-10.116322201480710748 + 8.6584007074554677485e-1130j 1.6e-494, 1.6e-494j
-9.6013568370968074116 - 9.2445358286952204992e-1128j 4.71e-494, 4.71e-494j
8.5177150397355443996 - 7.2532860669431482927e-1139j 1.93e-493, 1.93e-493j
9.1301035544069820442 + 6.3998076702842645331e-1176j 1.32e-493, 1.32e-493j
6.80585310157933011 - 4.4391605055859237281e-1200j 3.63e-494, 3.63e-494j
-14.162057069963751664 - 1.2141682886276260247e-1220j 1.81e-499, 1.81e-499j
2.536565579469149561 - 5.9012902335080819642e-1221j 2e-500, 2e-500j
1.3980661431208454968 + 1.7491374702645438544e-1225j 2e-504, 2e-504j
2.0622748805995499479 - 1.8942508374876141428e-1223j 5.99e-502, 5.99e-502j
-4.3486844940268798698 + 4.4043062426851143803e-1217j 1.47e-496, 1.47e-496j
9.6013568370968074116 - 4.0558416608447571262e-1213j 4.52e-494, 4.52e-494j
13.259521897775622893 - 1.4934100032280047857e-1228j 4.58e-498, 4.58e-498j
5.3351793308275412103 + 1.4815646320765098785e-1220j 3.01e-495, 3.01e-495j
-8.813517556249235824 - 2.335742439561377003e-1233j 2.34e-493, 2.34e-493j
-8.5177150397355443996 + 1.2766477952626865244e-1234j 2.04e-493, 2.04e-493j
-1.7367980813538412486 + 2.5853926860252441839e-1243j 3.19e-503, 3.19e-503j
-2.3344142183389772393 + 1.0462993916927231613e-1240j 5.93e-501, 5.93e-501j
3.7313022243357029508 - 6.8734317333048202627e-1235j 6.05e-497, 6.05e-497j
-5.696454565636292833 + 2.0793984897458720147e-1235j 6.22e-495, 6.22e-495j
-3.7313022243357029508 + 6.2173470439028639179e-1237j 5.84e-497, 5.84e-497j
-3.2242423501882442583 - 6.0932056642748056115e-1240j 7.15e-499, 7.15e-499j
-4.6962899838364346202 - 5.7876613123279214375e-1237j 5.32e-496, 5.32e-496j
-2.0622748805995499479 + 3.2393200911103389085e-1242j 5.51e-502, 5.51e-502j
1.0379709584894152952 + 4.9837638252021300839e-1246j 1.89e-505, 1.89e-505j
6.0626409716960507486 + 2.8917482888416816484e-1233j 1.34e-494, 1.34e-494j
5.0060619606307295585 + 6.2849387522405863266e-1250j 1.48e-495, 1.48e-495j
-0.8305587048553327679 + 4.1509868351155985013e-1290j 8.03e-506, 8.03e-506j
10.659960613843082338 - 1.4321096624200426693e-1278j 5.2e-495, 5.2e-495j
7.6417963208775787834 + 1.4175512486084611108e-1317j 7.93e-494, 7.93e-494j
1.7367980813538412486 - 5.9941707405478554224e-1360j 3.28e-503, 3.28e-503j
3.2242423501882442583 + 9.4514859319385037602e-1350j 7.61e-499, 7.61e-499j
12.512929139450520771 - 1.6047088729471162089e-1348j 4.62e-497, 4.62e-497j
-3.6332172365671085497 + 1.7663074429434931667e-1366j 2.78e-497, 2.78e-497j
-6.0626409716960507486 + 6.4118663098416003864e-1363j 1.21e-494, 1.21e-494j
0.8305587048553327679 + 2.0291712152450102317e-1391j 8.23e-506, 8.23e-506j
8.813517556249235824 - 2.0042701358783958232e-1378j 2.21e-493, 2.21e-493j
-1.3980661431208454968 + 2.4362833329136025093e-1409j 1.88e-504, 1.88e-504j
-10.659960613843082338 + 4.3269391404821416012e-1400j 4.88e-495, 4.88e-495j
-7.2122746971944838951 + 1.0419744578260333988e-1398j 4.73e-494, 4.73e-494j
-3.9605147105173808443 + 1.1586577698972531574e-1401j 6.46e-497, 6.46e-497j
3.6332172365671085497 + 8.1098292857626737438e-1398j 2.97e-497, 2.97e-497j
-6.4266528903044073058 + 1.3827693334118785542e-1405j 2.41e-494, 2.41e-494j
3.9605147105173808443 + 5.6827863029812474304e-1410j 6.28e-497, 6.28e-497j
-2.8536858288150520126 - 1.38638065352063461e-1430j 9.08e-500, 9.08e-500j
5.696454565636292833 + 2.7309259217299914268e-1446j 6.21e-495, 6.21e-495j
0.35872145743582179469 + 2.3189747232532903606e-1494j 1.21e-508, 1.21e-508j
-5.0060619606307295585 - 1.6093430878692585066e-1469j 1.37e-495, 1.37e-495j
-2.536565579469149561 + 1.3318296155139503293e-1481j 2.04e-500, 2.04e-500j
-0.74196378430272585765 - 1.8744294196847886037e-1493j 2.84e-506, 2.84e-506j
-7.6417963208775787834 + 1.7692352901840901727e-1478j 7.15e-494, 7.15e-494j
2.8536858288150520126 + 5.4352132213069878725e-1488j 9.41e-500, 9.41e-500j
0.74196378430272585765 - 2.306473651231532383e-1508j 2.72e-506, 2.72e-506j
-1.0379709584894152952 - 4.5721814546937801184e-1506j 1.97e-505, 1.97e-505j
-0.35872145743582179469 - 2.8229865496518836659e-1511j 1.35e-508, 1.35e-508j
3.2485920969704958018e-1511 + 2.784348103277787001e-1511j 3.12e-1509, 3.12e-1509j
8.085235231949366002 + 1.5767659156990909315e-1496j 1.16e-493, 1.16e-493j
4.3486844940268798698 + 1.5919662334736180204e-1525j 1.47e-496, 1.47e-496j
6.4266528903044073058 + 9.7848885685382487793e-1556j 2.3e-494, 2.3e-494j
7.2122746971944838951 - 1.3611260196701233263e-1581j 4.78e-494, 4.78e-494j

Weights

Weight (ball center) Error (ball radius)
1.2646220770809921714e-23 - 2.5091262631231942338e-1119j 3.88e-168, 2.52e-414j
9.2588137364287670023e-29 - 4.627855251563350865e-1125j 1.99e-172, 1.3e-418j
9.2588137364287670023e-29 + 8.837100250541629043e-1124j 1.2e-171, 7.79e-418j
1.1347748883137290329e-15 + 1.3104072518638584108e-1115j 7.44e-163, 4.84e-409j
9.1995373515814415388e-08 - 3.5144598972408172494e-1109j 1.08e-150, 7.05e-397j
1.1676876638155494364e-44 + 3.969277893225578797e-1134j 4.8e-180, 3.12e-426j
8.4279318547887374897e-32 - 6.1544061367434090884e-1126j 1.07e-173, 6.94e-420j
8.4279318547887374897e-32 + 4.8504872305716577317e-1127j 5.15e-175, 3.35e-421j
2.1309128867619860339e-39 + 9.2647969872988688171e-1132j 2.47e-179, 1.6e-425j
0.0054271248292481867701 - 5.2189070723584049996e-1104j 1.7e-132, 1.1e-378j
2.0979502920523799864e-06 - 2.0436003633800580455e-1107j 1.16e-151, 7.56e-398j
1.3477282391047375558e-19 - 3.3373177944437279302e-1118j 1.2e-168, 7.8e-415j
2.7935723997502670105e-35 - 3.1044197316636960904e-1129j 1.99e-177, 1.3e-423j
1.3696853336873039606e-11 - 1.4323658004717143768e-1112j 2.74e-162, 1.79e-408j
1.2646220770809921714e-23 - 1.6843742326463645256e-1121j 6.94e-172, 4.51e-418j
1.9099385088964823564e-21 + 7.8924212904408417476e-1120j 2.31e-170, 1.5e-416j
2.7934189083932486086e-17 - 2.0376224427256325263e-1115j 1.56e-172, 1.01e-418j
1.3477282391047375558e-19 - 6.5129004985201296066e-1117j 3.77e-174, 2.45e-420j
1.3696853336873039606e-11 - 7.3218460726698197055e-1112j 4.68e-168, 3.05e-414j
1.1676876638155494364e-44 - 6.6143813810165545435e-1135j 1.57e-185, 1.02e-431j
0.0040803887450728914456 + 3.1038669805114562979e-1104j 5.17e-145, 3.36e-391j
0.051958942767925024692 + 1.1158016443866984328e-1103j 3.9e-133, 2.54e-379j
0.014972643527457422642 + 5.6941996497476003513e-1104j 1.09e-140, 7.07e-387j
1.1519719413796109449e-05 + 3.259983675480522781e-1107j 1.04e-158, 6.75e-405j
1.9099385088964823564e-21 + 3.0219552749094920005e-1118j 1.06e-175, 6.89e-422j
2.1309128867619860339e-39 - 6.8901905954641585359e-1131j 2.71e-186, 1.77e-432j
9.1995373515814415388e-08 - 1.1357887426253242763e-1108j 5.54e-164, 3.6e-410j
1.2059447429097856701e-18 + 3.5851205070355202884e-1117j 1.08e-172, 7.04e-419j
2.7934189083932486086e-17 - 1.7480687554105771406e-1116j 3.12e-172, 2.03e-418j
0.029340158115223774386 - 4.8837212287186767099e-1104j 8.1e-146, 5.27e-392j
0.0054271248292481867701 - 3.2618997976241624582e-1104j 1.75e-151, 1.14e-397j
-8.3618603234898483625e-05 + 4.0957152830504067936e-1105j 6.31e-160, 4.11e-406j
1.3172788823410641891e-08 + 5.3643886299452990418e-1110j 7.75e-167, 5.04e-413j
-8.3618603234898483625e-05 + 1.8884989292797082224e-1105j 2.01e-160, 1.31e-406j
0.00084364855068587752943 + 1.6315253958779910437e-1105j 2.34e-158, 1.52e-404j
2.0979502920523799864e-06 - 7.4776681316690713941e-1108j 5.84e-164, 3.8e-410j
0.014972643527457422642 + 3.7657336984679173235e-1104j 1.53e-151, 9.96e-398j
0.091462980603384732079 - 3.7486335698474844391e-1103j 1.35e-143, 8.78e-390j
1.5144207410878745183e-09 - 3.2682889473480825228e-1110j 2.38e-172, 1.55e-418j
4.4607619585809524183e-07 + 5.5622136058920503022e-1108j 3.45e-168, 2.24e-414j
-0.06492847008112463701 + 9.6334983311592189297e-1103j 4.62e-146, 3e-392j
4.7013049472468080393e-26 - 1.1991779274126207681e-1121j 1.85e-184, 1.2e-430j
3.6466652705248900715e-14 - 9.5680843608430115534e-1114j 1.07e-177, 6.97e-424j
0.029340158115223774386 - 6.9081888569823977727e-1104j 1.48e-154, 9.6e-401j
0.00084364855068587752943 + 3.1580408718764972376e-1105j 2.53e-163, 1.64e-409j
2.7935723997502670105e-35 + 2.9312564027408504632e-1128j 4.45e-190, 2.89e-436j
0.000294865915495083693 - 2.1295921815480037253e-1105j 1.33e-164, 8.67e-411j
1.5144207410878745183e-09 - 8.1887828137017373392e-1111j 3e-173, 1.95e-419j
-0.06492847008112463701 + 1.1356821545402725252e-1102j 2.77e-154, 1.8e-400j
1.2059447429097856701e-18 + 5.2092043871029506172e-1116j 3.96e-180, 2.57e-426j
0.051958942767925024692 + 8.4484248357343900601e-1104j 3.6e-157, 2.34e-403j
4.7013049472468080393e-26 + 3.137804723259337447e-1123j 3.22e-185, 2.1e-431j
8.4746375710131961558e-13 + 1.4352372468961579047e-1113j 5.61e-177, 3.65e-423j
6.60542988137638071e-05 - 3.1826932096797185865e-1106j 9.16e-168, 5.96e-414j
0.000294865915495083693 - 4.5164950818347872618e-1105j 3.69e-169, 2.4e-415j
1.5781878890286095046e-10 + 1.1866491093129561172e-1111j 4.87e-175, 3.17e-421j
6.60542988137638071e-05 - 7.2780465150342732005e-1106j 7.4e-171, 4.81e-417j
0.0024158237025471411152 - 4.8631446140207712977e-1105j 3.68e-167, 2.39e-413j
1.3172788823410641891e-08 + 1.9191950279120809707e-1109j 4.01e-176, 2.61e-422j
0.13510425838216848516 + 1.8731489817332894885e-1103j 7.46e-164, 4.85e-410j
4.4607619585809524183e-07 + 1.879621542058897648e-1108j 8.02e-172, 5.22e-418j
0.0040803887450728914456 + 1.8593823564762714437e-1104j 6.85e-167, 4.45e-413j
0.15768605252142828157 - 8.1581731853297276458e-1103j 1.32e-164, 8.58e-411j
3.6466652705248900715e-14 - 1.3332759517019231599e-1114j 1.58e-178, 1.02e-424j
0.0024158237025471411152 - 8.6848661371513247318e-1105j 1.07e-169, 6.98e-416j
0.15768605252142828157 - 9.4495829609614948103e-1103j 4.03e-165, 2.62e-411j
0.091462980603384732079 - 3.0509698588438076528e-1103j 8.22e-166, 5.35e-412j
0.13510425838216848516 + 1.7448557249883267423e-1103j 3.36e-166, 2.18e-412j
0.14268995224804669401 - 1.472917896914717628e-1103j 2.51e-166, 1.63e-412j
1.1347748883137290329e-15 + 1.1743196239367070274e-1114j 2.55e-183, 1.66e-429j
1.1519719413796109449e-05 + 8.1759098072337088406e-1107j 2.11e-174, 1.37e-420j
1.5781878890286095046e-10 + 5.3204515108016604001e-1111j 6.22e-180, 4.06e-426j
8.4746375710131961558e-13 + 8.5641325334918840137e-1113j 6.98e-182, 4.53e-428j

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.