Rule: Q[8, 11, 64]

Type

This rule is of Hermite (physicists') 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)
-8.3088362680998387983 + 9.62340622716817787e-1068j 2.47e-492, 2.47e-492j
-8.6641513741329163529 - 3.2228096175558301546e-1067j 1.11e-492, 1.11e-492j
10.80036610091196226 + 2.4943788620203452682e-1067j 2.25e-496, 2.25e-496j
8.3088362680998387983 + 4.2522764973002723419e-1065j 2.39e-492, 2.39e-492j
-9.425596133793183464 + 1.3337837892881670727e-1081j 1.05e-493, 1.05e-493j
11.413700659149966297 + 3.3902419629208543473e-1085j 6.9e-498, 6.9e-498j
8.6641513741329163529 + 2.6775034310085481115e-1078j 1.03e-492, 1.03e-492j
-10.80036610091196226 + 4.1240084318038943243e-1102j 2.38e-496, 2.38e-496j
9.425596133793183464 + 1.2621934128638968006e-1098j 1.09e-493, 1.09e-493j
-9.841695636543860874 - 4.3860848208934356801e-1117j 2.17e-494, 2.17e-494j
1.6516370672192663114 - 2.2733291313967586269e-1141j 2.47e-501, 2.47e-501j
9.0350872064327151177 + 3.7338709930436392966e-1136j 3.76e-493, 3.76e-493j
6.6914308137357178479 - 1.7816267055947758682e-1177j 1.17e-491, 1.17e-491j
-1.8651745430168657961 + 1.0259905683620794702e-1211j 4.32e-500, 4.32e-500j
-4.7229543507335781425 + 6.0494245492867662115e-1201j 1.37e-492, 1.37e-492j
2.4338784655073942623 - 2.4234228724792501525e-1212j 2.17e-498, 2.17e-498j
3.1750669775496321913 + 1.0653579665691186523e-1205j 5.53e-496, 5.53e-496j
9.841695636543860874 + 3.8770712075550977989e-1224j 2.11e-494, 2.11e-494j
-2.6827949498805141598 - 1.2699240296899514463e-1251j 1.33e-497, 1.33e-497j
-1.6516370672192663114 + 8.6552351862744568699e-1263j 2.43e-501, 2.43e-501j
7.3124612560894450638 - 5.1460434922908829571e-1261j 9.4e-492, 9.4e-492j
1.1571937124467801947 + 1.4902215944566210455e-1292j 7.55e-504, 7.55e-504j
-6.3911243983966872588 - 7.9760539022726234314e-1281j 1.06e-491, 1.06e-491j
-4.0851426488710547321 + 9.5140448770344612807e-1286j 2.12e-493, 2.12e-493j
-3.8734392208149045564 - 5.7627921562372554542e-1288j 6.08e-494, 6.08e-494j
4.9809915111937402339 - 3.8823062488152792301e-1289j 2.24e-492, 2.24e-492j
0.9115581854504433438 + 3.8659083086164849696e-1320j 5.52e-505, 5.52e-505j
-10.293438881816412992 + 3.545582584613386083e-1306j 2.89e-495, 2.89e-495j
-7.3124612560894450638 + 1.1147740958401135891e-1315j 9.93e-492, 9.93e-492j
-2.1885630273880580333 - 8.5731494575727464869e-1335j 3.99e-499, 3.99e-499j
6.3911243983966872588 - 3.9816954951490148527e-1352j 1.1e-491, 1.1e-491j
7.6347600963786953869 - 1.9015958682388910936e-1397j 7.13e-492, 7.13e-492j
-11.413700659149966297 + 2.1477488576246300818e-1428j 7.46e-498, 7.46e-498j
-7.9663786144738472445 - 5.478443774521895465e-1421j 4.26e-492, 4.26e-492j
-4.9809915111937402339 + 4.443785110915524835e-1424j 2.1e-492, 2.1e-492j
7.9663786144738472445 - 2.256646603913387302e-1435j 4.47e-492, 4.47e-492j
5.8085478715650011978 - 7.2524255267254555548e-1458j 7e-492, 7e-492j
1.8651745430168657961 - 8.3139390790237774634e-1477j 4.04e-500, 4.04e-500j
3.6473028998600486888 - 4.5479305890796221625e-1471j 1.46e-494, 1.46e-494j
-5.2497426940464991728 - 1.6745314256157577108e-1469j 3.31e-492, 3.31e-492j
-0.6890661139269487337 - 8.7011405737528850846e-1482j 7.76e-506, 7.76e-506j
-4.2768786658771216712 + 1.7109759998241265981e-1469j 5.09e-493, 5.09e-493j
4.2768786658771216712 - 1.099363844051099473e-1467j 4.98e-493, 4.98e-493j
-0.9115581854504433438 - 3.3852901784462305188e-1491j 5.45e-505, 5.45e-505j
4.0851426488710547321 + 1.6063263947260266817e-1477j 2.13e-493, 2.13e-493j
3.4142315838912480547 - 5.4053362766530667749e-1487j 2.87e-495, 2.87e-495j
-9.0350872064327151177 - 2.4890941261799324972e-1484j 3.73e-493, 3.73e-493j
4.7229543507335781425 + 1.0793973726071397111e-1484j 1.32e-492, 1.32e-492j
5.5260127615574376054 + 1.2796550725433738097e-1504j 4.92e-492, 4.92e-492j
10.293438881816412992 + 3.6387197701873356771e-1517j 2.77e-495, 2.77e-495j
-5.8085478715650011978 + 1.7442654880439750926e-1519j 7.22e-492, 7.22e-492j
-1.4058263375320000493 - 3.1299983186041542438e-1531j 1.23e-502, 1.23e-502j
-5.5260127615574376054 - 4.158894119741528444e-1520j 5.15e-492, 5.15e-492j
-6.6914308137357178479 + 5.4628166520295388818e-1519j 1.16e-491, 1.16e-491j
1.4058263375320000493 - 1.3312153947932874046e-1534j 1.23e-502, 1.23e-502j
-3.6473028998600486888 - 1.6138364292843957576e-1526j 1.5e-494, 1.5e-494j
-3.1750669775496321913 + 1.056669938006744039e-1529j 5.12e-496, 5.12e-496j
2.1885630273880580333 + 3.0903275876826183564e-1530j 4.01e-499, 4.01e-499j
1.9816567566958429259 - 5.1489612796857853836e-1531j 1.3e-499, 1.3e-499j
0.6890661139269487337 + 7.7232566318778460769e-1538j 7.12e-506, 7.12e-506j
-7.6347600963786953869 - 1.2576520519637245037e-1521j 6.82e-492, 6.82e-492j
-2.4338784655073942623 - 1.8758778480090891094e-1537j 2.05e-498, 2.05e-498j
-1.1571937124467801947 + 3.9099549138555712655e-1543j 7.79e-504, 7.79e-504j
6.9983171303826563552 - 4.3044860977009056739e-1530j 1.14e-491, 1.14e-491j
5.2497426940464991728 - 5.4938179445380417015e-1541j 3.56e-492, 3.56e-492j
2.6827949498805141598 - 3.1610283510908241533e-1555j 1.29e-497, 1.29e-497j
-6.9983171303826563552 + 1.3562859126657855545e-1549j 1.16e-491, 1.16e-491j
-1.9816567566958429259 + 2.0186220159317845219e-1559j 1.32e-499, 1.32e-499j
-3.4142315838912480547 + 1.6860605853476261973e-1553j 2.77e-495, 2.77e-495j
2.9306374202572440192 - 6.4961804794649335642e-1555j 8.83e-497, 8.83e-497j
0.38118699020732211685 + 2.7528811243375361263e-1565j 9.23e-508, 9.23e-508j
6.0969192900900611708 - 4.8059625153078161357e-1548j 9.46e-492, 9.46e-492j
-0.15847281797957421666 + 4.9860499723093272892e-1575j 3.18e-509, 3.18e-509j
-6.0969192900900611708 + 9.0563182999352069343e-1558j 9.03e-492, 9.03e-492j
-1.8151725193789957695e-1612 - 9.1729157780103629454e-1613j 1.69e-1610, 1.69e-1610j
3.8734392208149045564 - 7.3499961968990536538e-1560j 6.45e-494, 6.45e-494j
4.4838301627422905975 - 5.9678652608149917068e-1557j 8.74e-493, 8.74e-493j
-4.4838301627422905975 - 2.0884238644751418977e-1561j 8.61e-493, 8.61e-493j
-0.38118699020732211685 + 4.1076922258259283994e-1576j 9.29e-508, 9.29e-508j
-2.9306374202572440192 + 1.6694002430586164642e-1565j 8.45e-497, 8.45e-497j
-0.56474674797970907162 + 1.7255966736383683137e-1574j 1.95e-506, 1.95e-506j
0.56474674797970907162 + 5.2404033037936674212e-1575j 1.9e-506, 1.9e-506j
0.15847281797957421666 - 1.6270574966378677113e-1577j 3.18e-509, 3.18e-509j

Weights

Weight (ball center) Error (ball radius)
2.0480565188754178309e-31 - 3.2176006022946545418e-1097j 2.2e-163, 9.25e-409j
5.1218407125058198483e-34 + 1.6934160700150804155e-1098j 6.89e-165, 2.89e-410j
6.74951125211134546e-52 + 1.4847333760984570124e-1107j 1.14e-174, 4.77e-420j
2.0480565188754178309e-31 - 8.3105502766041600651e-1095j 6.15e-166, 2.58e-411j
5.9181450150383572857e-40 + 7.7724833172120085217e-1102j 6.47e-170, 2.72e-415j
1.0605937370724814591e-57 - 8.7725086536979912218e-1111j 4.36e-177, 1.83e-422j
5.1218407125058198483e-34 - 8.0002608552909800216e-1097j 1.22e-167, 5.12e-413j
6.74951125211134546e-52 - 1.9787779420863508236e-1108j 5.08e-177, 2.13e-422j
5.9181450150383572857e-40 - 1.1763244150984961518e-1100j 4.57e-171, 1.92e-416j
2.0957063654368029323e-43 - 9.2048209604588368252e-1104j 1.98e-173, 8.3e-419j
0.0088716967513372364347 - 3.9853668358798975258e-1077j 8.12e-120, 3.41e-365j
7.5588480618937130014e-37 + 9.8571438754702708195e-1099j 1.63e-169, 6.84e-415j
6.1367948045329940205e-21 + 9.4073892355617647821e-1090j 1.15e-162, 4.84e-408j
0.002727867736927326899 + 2.8399097024165225445e-1077j 1.99e-126, 8.36e-372j
2.9035432829505253957e-11 - 7.960713904474266546e-1084j 2.48e-154, 1.04e-399j
0.00037490757469988068465 - 2.0354599249376341177e-1078j 3.38e-134, 1.42e-379j
5.7171542038917779854e-06 + 9.4132970913601986349e-1080j 3.32e-142, 1.39e-387j
2.0957063654368029323e-43 + 1.0525721575249032577e-1102j 3.07e-173, 1.29e-418j
0.00010508179267642267021 + 3.3664153459043371843e-1079j 2.79e-139, 1.17e-384j
0.0088716967513372364347 - 2.6574657514581782579e-1077j 2.13e-125, 8.96e-371j
1.0747055660231125978e-24 + 7.6350685813414677409e-1092j 1.98e-165, 8.32e-411j
0.036689760127904025961 - 9.2223133096159113184e-1077j 2.91e-117, 1.22e-362j
3.0553856513135319037e-19 - 1.205880938082318381e-1089j 1.04e-164, 4.35e-410j
6.3758557054351905819e-09 + 8.8024822136090068627e-1082j 5.64e-152, 2.37e-397j
3.8030505015657418585e-08 - 2.3389671198580535007e-1081j 1.27e-150, 5.35e-396j
2.5025338390981203872e-12 + 3.9569998636419253786e-1084j 1.16e-158, 4.85e-404j
0.05928219315562899617 + 2.2439392144572145234e-1076j 1.43e-121, 5.99e-367j
2.5838889176141577119e-47 + 6.3768770002885376504e-1106j 3.92e-179, 1.65e-424j
1.0747055660231125978e-24 + 4.6652528704152006997e-1093j 2.84e-169, 1.19e-414j
0.0011216918664061762022 + 4.5447362194825774149e-1078j 4.83e-138, 2.03e-383j
3.0553856513135319037e-19 - 9.439304114727051322e-1089j 3.96e-165, 1.66e-410j
8.9287471072210494034e-27 - 6.5001868170803637234e-1093j 5.32e-169, 2.23e-414j
1.0605937370724814591e-57 + 1.4060105116479376249e-1111j 9.47e-185, 3.98e-430j
5.2121796348493248142e-29 + 1.1584334610063966719e-1095j 8.56e-172, 3.6e-417j
2.5025338390981203872e-12 + 9.8051729632601815756e-1085j 1.56e-160, 6.54e-406j
5.2121796348493248142e-29 + 6.2636174486538293571e-1094j 1.41e-170, 5.91e-416j
3.5829641608552262971e-16 - 7.7754986962269690033e-1087j 4.93e-165, 2.07e-410j
0.002727867736927326899 + 4.4959349399583344554e-1077j 5e-142, 2.1e-387j
2.1666291789813445918e-07 + 1.5718801530781991529e-1080j 2.31e-156, 9.71e-402j
1.6528713767728808938e-13 - 1.1491206383632095985e-1085j 1.66e-163, 6.96e-409j
0.064063626725002173482 - 6.5492121996893706735e-1076j 3.03e-136, 1.27e-381j
1.2293709998517864682e-09 - 2.7928272412798827899e-1082j 2.31e-158, 9.72e-404j
1.2293709998517864682e-09 - 8.7865930329579376599e-1082j 3.37e-160, 1.41e-405j
0.05928219315562899617 + 1.7980024013331689664e-1076j 1.17e-137, 4.92e-383j
6.3758557054351905819e-09 + 2.6018740412448793237e-1081j 2.49e-159, 1.05e-404j
1.1535662400227943726e-06 - 3.8232972911235958601e-1080j 3.91e-156, 1.64e-401j
7.5588480618937130014e-37 - 4.4621564404895877128e-1100j 1.71e-179, 7.19e-425j
2.9035432829505253957e-11 - 2.9204536859426899748e-1083j 1.02e-162, 4.28e-408j
8.627230064983422208e-15 + 6.4739959971222902648e-1086j 3.73e-166, 1.57e-411j
2.5838889176141577119e-47 - 5.8170781440608603702e-1105j 5.74e-184, 2.41e-429j
3.5829641608552262971e-16 - 1.3562249268696663659e-1087j 1.04e-170, 4.38e-416j
0.019420901044245486861 + 3.6589409924575836454e-1077j 4.88e-149, 2.05e-394j
8.627230064983422208e-15 + 1.2849638528693406542e-1086j 2.34e-169, 9.82e-415j
6.1367948045329940205e-21 + 9.8888543818745470797e-1091j 2.01e-174, 8.43e-420j
0.019420901044245486861 + 5.1593694722534548529e-1077j 1.95e-151, 8.21e-397j
2.1666291789813445918e-07 + 6.0912020995085420797e-1081j 2.37e-163, 9.97e-409j
5.7171542038917779854e-06 + 4.1869988734098348896e-1080j 3.08e-162, 1.29e-407j
0.0011216918664061762022 + 7.819940172112867696e-1078j 1.62e-157, 6.79e-403j
0.0015954012829624161312 - 3.1871566729963517714e-1077j 5.19e-156, 2.18e-401j
0.064063626725002173482 - 7.7409991916677800509e-1076j 1.27e-151, 5.32e-397j
8.9287471072210494034e-27 - 2.5766841243151800195e-1094j 2.04e-178, 8.57e-424j
0.00037490757469988068465 - 1.1091414930072335025e-1078j 3.92e-160, 1.64e-405j
0.036689760127904025961 - 6.9563754686146915923e-1077j 1.04e-154, 4.39e-400j
9.3999848466084797344e-23 - 8.740439798148953106e-1091j 3.27e-176, 1.37e-421j
1.6528713767728808938e-13 - 5.1534827091626042103e-1085j 1.4e-170, 5.9e-416j
0.00010508179267642267021 + 6.6037192367300108585e-1079j 2.11e-162, 8.86e-408j
9.3999848466084797344e-23 - 7.2471300341097434304e-1092j 5.01e-177, 2.11e-422j
0.0015954012829624161312 - 1.9540730836050822509e-1077j 4.13e-160, 1.73e-405j
1.1535662400227943726e-06 - 1.5874505939538650285e-1080j 2.94e-165, 1.24e-410j
2.5895530038728769549e-05 - 2.4080567432708133792e-1079j 5.35e-164, 2.25e-409j
0.10932993981225860799 - 1.069869899899432249e-1075j 2.11e-159, 8.88e-405j
1.1801347274055225983e-17 + 8.8414102510784249721e-1088j 4e-174, 1.68e-419j
0.11388778612497470487 + 1.3494870497351714124e-1075j 2e-160, 8.38e-406j
1.1801347274055225983e-17 + 1.3336918348748811656e-1088j 1.21e-174, 5.08e-420j
0.068051349943459864373 - 1.7536493523437689242e-1075j 1.84e-160, 7.74e-406j
3.8030505015657418585e-08 - 6.4673520791968217618e-1081j 2.78e-167, 1.17e-412j
2.3543133460670771175e-10 + 1.9260483703831297524e-1082j 5.34e-169, 2.24e-414j
2.3543133460670771175e-10 + 5.7098881929297806196e-1083j 6.27e-170, 2.63e-415j
0.10932993981225860799 - 9.7550504442169075455e-1076j 9.95e-163, 4.17e-408j
2.5895530038728769549e-05 - 1.1470685675253099523e-1079j 4.86e-167, 2.05e-412j
0.048470442216970764986 + 1.015600754826564985e-1075j 9.5e-163, 3.98e-408j
0.048470442216970764986 + 1.1646240626213744251e-1075j 2.17e-163, 9.32e-409j
0.11388778612497470487 + 1.4022663510278987709e-1075j 3.02e-163, 1.22e-408j

Download

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