Rule: Q[1, 8, 14, 70]

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)
-13.806180649380667315 + 4.5794111238863996038e-1748j 1.23e-491, 1.23e-491j
-15.549485024755451504 + 1.4158015226686189156e-1752j 6.82e-494, 6.82e-494j
16.2523592514043197 - 3.361450700951487453e-1754j 4.96e-495, 4.96e-495j
-17.10326012360274821 + 1.920455151215002733e-1756j 1.29e-496, 1.29e-496j
-5.9138640831936987203 + 4.11754610917239909e-1748j 4.66e-492, 4.66e-492j
-8.9349968363174726541 + 1.9109016786452522226e-1747j 5.87e-490, 5.87e-490j
11.42133604527585482 + 6.0989253305032866849e-1761j 6.64e-490, 6.64e-490j
-13.292610653294220703 + 1.4912536088455564825e-1777j 3.98e-491, 3.98e-491j
-14.346986671221196439 + 1.3811617614635488984e-1778j 3.21e-492, 3.21e-492j
5.3503187718549218936 - 3.0187555300958076178e-1778j 1.79e-491, 1.79e-491j
-10.560543899189514223 + 1.3484569822200126075e-1775j 1.1e-489, 1.1e-489j
14.346986671221196439 - 1.5670338626547176527e-1777j 3.07e-492, 3.07e-492j
-11.867633543221163439 - 1.1738293420244513607e-1777j 4.26e-490, 4.26e-490j
10.143533711208621696 - 4.8646367210708324392e-1785j 1e-489, 1e-489j
14.923421840757168739 + 2.386481083145111058e-1803j 5.81e-493, 5.81e-493j
-12.800748259011811956 - 3.5554040226884496782e-1801j 1.1e-490, 1.1e-490j
10.986100018282196241 + 6.522027800755901377e-1799j 8.77e-490, 8.77e-490j
3.6724605356604560933 - 2.2484886081614873773e-1814j 5.41e-495, 5.41e-495j
13.292610653294220703 + 1.6799890522580288417e-1808j 3.99e-491, 3.99e-491j
-2.7388322698689555103 - 1.3881617846803459235e-1826j 9.45e-499, 9.45e-499j
-4.874801837805208452 + 8.7564191260668141242e-1822j 1.32e-493, 1.32e-493j
8.5439868547891694894 + 8.0228025839923480226e-1817j 3.5e-490, 3.5e-490j
12.326709433970975515 - 1.3182038217995944086e-1832j 2.22e-490, 2.22e-490j
-5.502828334987505698 - 4.1230287163520327233e-1846j 6.82e-492, 6.82e-492j
-1.323547725164135155 - 5.4192880882623027268e-1858j 8.93e-504, 8.93e-504j
13.806180649380667315 - 6.3251582663655746738e-1844j 1.21e-491, 1.21e-491j
-16.2523592514043197 + 1.5940675940223045323e-1849j 4.53e-495, 4.53e-495j
17.10326012360274821 + 4.9012818555322472458e-1852j 1.31e-496, 1.31e-496j
-10.143533711208621696 + 1.3912372408850559371e-1843j 1.04e-489, 1.04e-489j
-14.923421840757168739 + 6.5432535139759883075e-1852j 5.72e-493, 5.72e-493j
9.7341225418111100194 - 3.9743875969475164082e-1847j 9.27e-490, 9.27e-490j
3.7621859351467819782 + 4.6393210969375393274e-1865j 5.53e-495, 5.53e-495j
-11.42133604527585482 - 1.5914527149479936176e-1858j 6.48e-490, 6.48e-490j
4.5127458633997826676 + 9.266719713151137563e-1865j 2.18e-494, 2.18e-494j
-3.2054290028564699434 - 3.8608865074451743371e-1867j 6.79e-497, 6.79e-497j
-7.0247239051874141176 - 5.3900647574508127001e-1863j 3.55e-491, 3.55e-491j
12.800748259011811956 - 2.539846256007614107e-1860j 1.06e-490, 1.06e-490j
-9.7341225418111100194 + 3.0133615742734070402e-1867j 8.88e-490, 8.88e-490j
7.7763626753230505988 + 8.5191323044631890845e-1869j 1.31e-490, 1.31e-490j
8.157939380593504462 + 2.1244265105413611755e-1884j 2.16e-490, 2.16e-490j
-4.5127458633997826676 + 3.4804832311129358098e-1895j 2.25e-494, 2.25e-494j
-2.4102429301348709313 + 3.8666821835094658738e-1903j 4.49e-500, 4.49e-500j
5.310191817728151108 + 2.9091979583278421888e-1891j 1.33e-491, 1.33e-491j
-8.5439868547891694894 - 1.5580778497204701113e-1889j 3.44e-490, 3.44e-490j
15.549485024755451504 - 1.1661108145433175124e-1894j 7.27e-494, 7.27e-494j
-3.7621859351467819782 - 1.5719335592344919571e-1895j 5.66e-495, 5.66e-495j
1.7556551274300274783 - 7.2220457201300094005e-1903j 3.06e-502, 3.06e-502j
5.9138640831936987203 - 1.3593528534276994825e-1890j 4.36e-492, 4.36e-492j
-10.986100018282196241 + 1.2007745506567498594e-1891j 8.48e-490, 8.48e-490j
1.5171446301536223065 - 1.6221556355430758614e-1907j 5.96e-503, 5.96e-503j
-9.3315073251315922703 + 2.2888475793931754247e-1894j 8.02e-490, 8.02e-490j
-0.64305331156372658316 - 1.3860265458696119337e-1912j 1.28e-506, 1.28e-506j
-6.284301980867298391 - 3.2103022865505837036e-1897j 7.88e-492, 7.88e-492j
6.284301980867298391 - 3.798248744547408685e-1897j 8.3e-492, 8.3e-492j
1.323547725164135155 - 2.8790235809967575128e-1918j 9.74e-504, 9.74e-504j
-6.6535711713698961258 - 6.7326944182752542567e-1903j 1.64e-491, 1.64e-491j
-1.5171446301536223065 - 2.0833742716220906447e-1922j 6.26e-503, 6.26e-503j
-4.1547882422826199878 - 4.6322067560110254609e-1914j 5.37e-495, 5.37e-495j
3.0124014398723451999 - 1.4728877372895215093e-1917j 1.32e-497, 1.32e-497j
-5.3503187718549218936 - 1.2326973281335635971e-1909j 1.83e-491, 1.83e-491j
11.867633543221163439 + 3.7419637406118140196e-1913j 4.18e-490, 4.18e-490j
-8.157939380593504462 - 3.2794922527925817016e-1927j 2.1e-490, 2.1e-490j
-1.7556551274300274783 + 2.991232046704118228e-1940j 3.08e-502, 3.08e-502j
-12.326709433970975515 - 5.2985329988111015032e-1928j 2.26e-490, 2.26e-490j
-3.5339390047676755605 - 6.5080205791270374902e-1934j 1.36e-495, 1.36e-495j
0.33308698865191950329 + 7.0521549865739781171e-1949j 1.85e-508, 1.85e-508j
-5.310191817728151108 + 2.2217465010260367005e-1928j 1.42e-491, 1.42e-491j
4.1547882422826199878 + 5.8132327439065306756e-1934j 5.24e-495, 5.24e-495j
-7.7763626753230505988 - 1.541207234727050729e-1927j 1.28e-490, 1.28e-490j
10.560543899189514223 - 5.8258882849440432762e-1930j 1e-489, 1e-489j
4.874801837805208452 - 6.931209074434530766e-1952j 1.29e-493, 1.29e-493j
9.3315073251315922703 - 1.1134903778992739436e-1947j 7.63e-490, 7.63e-490j
7.0247239051874141176 - 1.2255722294780218251e-1958j 3.64e-491, 3.64e-491j
3.2054290028564699434 - 9.8171104600840229356e-1974j 6.74e-497, 6.74e-497j
8.9349968363174726541 + 9.8721071717146000082e-1968j 5.62e-490, 5.62e-490j
0.76977736021945725517 + 1.8320119962584823611e-1992j 6.05e-506, 6.05e-506j
-3.6724605356604560933 + 6.0365434678067794321e-1983j 5.15e-495, 5.15e-495j
-2.0768479786778301065 - 2.000244798151523338e-1988j 3.37e-501, 3.37e-501j
-1.0232556637891325248 + 6.5323783563921666086e-1992j 4.34e-505, 4.34e-505j
2.0768479786778301065 + 1.1092227024131716293e-1987j 3.22e-501, 3.22e-501j
1.0232556637891325248 - 3.835099435565800012e-1992j 5.03e-505, 5.03e-505j
3.5339390047676755605 - 4.7145470438506382433e-1982j 1.22e-495, 1.22e-495j
2.7388322698689555103 - 1.4863483962094455049e-1985j 8.75e-499, 8.75e-499j
-7.3987869910806868942 + 9.3388159710491017434e-1979j 6.95e-491, 6.95e-491j
-0.76977736021945725517 - 2.3475560008651071929e-1992j 6.28e-506, 6.28e-506j
7.3987869910806868942 + 2.6557580405813938515e-1976j 6.77e-491, 6.77e-491j
6.6535711713698961258 + 1.8266799709723576043e-1991j 1.65e-491, 1.65e-491j
0.64305331156372658316 + 3.0866319142603323435e-2008j 1.25e-506, 1.25e-506j
-3.0124014398723451999 + 1.5070024594739787558e-2001j 1.49e-497, 1.49e-497j
-0.33308698865191950329 - 1.0470771088278647351e-2010j 1.72e-508, 1.72e-508j
5.502828334987505698 - 7.8169332052961345005e-2008j 6.93e-492, 6.93e-492j
2.4102429301348709313 + 4.5488091945851468709e-2016j 4.38e-500, 4.38e-500j
2.7366361644401341704e-2279 - 7.3977051462762920771e-2279j 7.34e-2277, 7.34e-2277j

Weights

Weight (ball center) Error (ball radius)
8.5387400595067808408e-43 + 4.56506492480075509e-1779j 1.41e-148, 3.8e-392j
8.2401250798149581712e-54 - 3.0686491524226313701e-1785j 1.2e-153, 3.25e-397j
1.3281573178624352176e-58 - 3.2270168373635095383e-1788j 7.08e-158, 1.91e-401j
1.1851430718320109193e-64 - 3.4774296501808973116e-1791j 7.57e-158, 2.05e-401j
3.7960891777646511173e-09 + 1.0471368348690882765e-1755j 1.83e-118, 4.93e-362j
7.2488352625997592206e-19 - 8.1801693820782352161e-1765j 5.65e-134, 1.53e-377j
8.2923904346241244338e-30 + 5.4292582959324462703e-1772j 5.74e-146, 1.55e-389j
8.5718155391195797355e-40 - 2.372307132918490335e-1777j 4.75e-148, 1.28e-391j
4.4663419851439853475e-46 - 6.3460818175368970906e-1781j 8.81e-151, 2.38e-394j
-4.0895473362467138482e-07 + 5.9179951755222987561e-1755j 4.44e-120, 1.2e-363j
1.0184554827970860208e-25 - 5.8555888408536376281e-1769j 3.26e-141, 8.81e-385j
4.4663419851439853475e-46 + 2.5923413475690007215e-1781j 2.27e-156, 6.14e-400j
4.7122235864444675752e-32 + 7.9376027981812585444e-1773j 1.95e-145, 5.27e-389j
7.4881209576910258897e-24 - 2.204930521845951338e-1768j 2.27e-144, 6.13e-388j
1.040461637881476014e-49 - 2.4792493422663756123e-1783j 4.56e-158, 1.23e-401j
5.0437870382628133466e-37 + 9.4514892884175673339e-1776j 1.4e-148, 3.78e-392j
1.061975801341849037e-27 - 9.8541437908785865917e-1771j 3.63e-147, 9.8e-391j
-0.00024142248714021624382 + 4.7189896952866221656e-1752j 2.24e-113, 6.06e-357j
8.5718155391195797355e-40 + 8.910599834407242097e-1778j 1.99e-154, 5.37e-398j
0.0029789097937157422895 + 1.7276758046151678855e-1751j 1.59e-105, 4.3e-349j
1.0158176248344026887e-06 + 2.4785327513565437727e-1754j 4.22e-123, 1.14e-366j
2.1804800923448486561e-17 - 3.3147214032093418331e-1764j 1.82e-141, 4.91e-385j
1.8810207957616223117e-34 + 1.029981973150803188e-1774j 4.27e-152, 1.15e-395j
6.7572303631139756775e-08 - 1.7243821538122718107e-1754j 6.76e-128, 1.83e-371j
0.043885237003783643783 - 2.666307090959918743e-1750j 3.94e-88, 1.06e-331j
8.5387400595067808408e-43 - 1.7899309057179367975e-1779j 7.44e-156, 2.01e-399j
1.3281573178624352176e-58 + 7.020281466770884403e-1788j 8.73e-163, 2.36e-406j
1.1851430718320109193e-64 + 1.6682015209777219464e-1791j 1.03e-166, 2.78e-410j
7.4881209576910258897e-24 + 8.9834380410587863154e-1768j 4.97e-147, 1.34e-390j
1.040461637881476014e-49 + 5.8335647312949183205e-1783j 9.69e-159, 2.62e-402j
4.3046188020560284082e-22 + 2.7908992756674299662e-1767j 2.34e-147, 6.32e-391j
0.00021959477865959266639 - 2.1302318361067742665e-1752j 1.04e-122, 2.8e-366j
8.2923904346241244338e-30 - 1.7730457412778451177e-1771j 2.11e-150, 5.7e-394j
5.4097408151934870102e-06 - 9.5530879089624942777e-1755j 1.21e-128, 3.26e-372j
0.00057078811242056419325 + 1.6081581340802570934e-1751j 5.99e-120, 1.62e-363j
2.8609759952221238923e-12 + 2.0230322872245288793e-1759j 1.37e-139, 3.69e-383j
5.0437870382628133466e-37 - 3.3921652452522484952e-1776j 2.9e-155, 7.84e-399j
4.3046188020560284082e-22 - 1.2672786760310480754e-1766j 8.55e-147, 2.31e-390j
1.1190040441435464691e-14 - 2.6435086462874451253e-1762j 4.76e-144, 1.29e-387j
5.4120448377515413944e-16 + 3.0402723166748412072e-1763j 8.37e-145, 2.26e-388j
5.4097408151934870102e-06 - 7.0191392348918942336e-1754j 7.55e-131, 2.04e-374j
0.0072921414973826526967 - 1.9896694126762905947e-1751j 1.02e-117, 2.75e-361j
5.1489039558267227642e-07 - 5.9301684159042041492e-1755j 6.32e-135, 1.71e-378j
2.1804800923448486561e-17 + 1.4429650052103364658e-1763j 7.94e-146, 2.15e-389j
8.2401250798149581712e-54 + 1.3559796338457692269e-1785j 3.17e-165, 8.56e-409j
0.00021959477865959266639 - 9.4881091350582474595e-1752j 1.2e-128, 3.23e-372j
0.025813368479080459094 - 5.1728320825680307747e-1751j 5.28e-117, 1.43e-360j
3.7960891777646511173e-09 + 1.3511927732714327929e-1757j 2.03e-139, 5.49e-383j
1.061975801341849037e-27 + 3.4301081239845840973e-1770j 2.35e-151, 6.35e-395j
0.020859433103418951618 + 1.2898286936195150364e-1750j 9.84e-116, 2.66e-359j
1.9671706352676016765e-20 + 1.7383389991381797532e-1765j 1.89e-147, 5.09e-391j
0.081446399303909061323 + 5.6341173753496409976e-1750j 2.64e-114, 7.13e-358j
3.9103563343030619462e-10 + 4.1391212421830503737e-1757j 2.34e-140, 6.33e-384j
3.9103563343030619462e-10 - 1.2904653885399294698e-1758j 2.26e-143, 6.11e-387j
0.043885237003783643783 - 1.6959016905875285611e-1750j 2.68e-116, 7.25e-360j
3.5972249153377908244e-11 - 2.4442577339183855147e-1758j 9.96e-142, 2.69e-385j
0.020859433103418951618 + 2.1728496926539283214e-1750j 1.65e-119, 4.45e-363j
2.558739190523962558e-05 + 3.2561484871586000387e-1753j 7.04e-134, 1.9e-377j
0.00087593849822056169631 - 6.5752189679092947117e-1752j 6.21e-133, 1.68e-376j
-4.0895473362467138482e-07 + 1.1622998548118360133e-1753j 1.61e-137, 4.35e-381j
4.7122235864444675752e-32 - 2.574448834011442333e-1773j 1.43e-159, 3.87e-403j
5.4120448377515413944e-16 - 1.7115271038484999264e-1762j 2.26e-147, 6.1e-391j
0.025813368479080459094 - 9.5044830708863785563e-1751j 4.23e-126, 1.14e-369j
1.8810207957616223117e-34 - 3.0129434675450094598e-1774j 3.57e-158, 9.63e-402j
0.00038153797579059000784 - 1.5808700532583854978e-1751j 3.74e-134, 1.01e-377j
0.12458060229230839051 - 1.7650000529143605588e-1750j 7.28e-126, 1.97e-369j
5.1489039558267227642e-07 - 1.0837002813038491581e-1753j 9.84e-138, 2.66e-381j
2.558739190523962558e-05 + 5.7524355841091737592e-1754j 1.52e-141, 4.1e-385j
1.1190040441435464691e-14 + 1.8131789417264508154e-1761j 6.28e-147, 1.7e-390j
1.0184554827970860208e-25 + 1.5648421065307319111e-1769j 8.61e-159, 2.33e-402j
1.0158176248344026887e-06 + 2.4221840290919624717e-1755j 9.34e-145, 2.52e-388j
1.9671706352676016765e-20 - 3.2089354380468923027e-1766j 7.33e-157, 1.98e-400j
2.8609759952221238923e-12 - 1.8062036895975739463e-1760j 9.8e-153, 2.65e-396j
0.00057078811242056419325 + 4.813234335710195437e-1752j 2.43e-142, 6.58e-386j
7.2488352625997592206e-19 + 3.3867541967490800394e-1765j 3.34e-156, 9.01e-400j
0.035366156878371625593 - 4.940079781825347131e-1750j 1.23e-135, 3.31e-379j
-0.00024142248714021624382 + 1.9996495261198826608e-1751j 2.63e-140, 7.09e-384j
0.015282751638641613113 + 3.5297605282721995487e-1751j 3.13e-138, 8.46e-382j
0.073968650706209636148 + 3.2172682423445106243e-1750j 4.59e-136, 1.24e-379j
0.015282751638641613113 + 1.7027522266467616556e-1751j 8.56e-141, 2.31e-384j
0.073968650706209636148 + 2.2730773583395802383e-1750j 1.32e-137, 3.56e-381j
0.00038153797579059000784 - 4.0174072520644661163e-1752j 3.87e-143, 1.05e-386j
0.0029789097937157422895 + 6.3798600592076233127e-1752j 9.67e-143, 2.61e-386j
1.9440383210947928485e-13 - 1.88317050807261357e-1760j 4.3e-152, 1.16e-395j
0.035366156878371625593 - 6.4081600002067805706e-1750j 2.21e-139, 5.97e-383j
1.9440383210947928485e-13 + 2.2089819457805231117e-1761j 3.59e-154, 9.69e-398j
3.5972249153377908244e-11 + 1.4849338607970724326e-1759j 1.31e-152, 3.53e-396j
0.081446399303909061323 + 4.5351494227652561659e-1750j 6.6e-142, 1.78e-385j
0.00087593849822056169631 - 2.0084814131718236292e-1751j 4.14e-144, 1.11e-387j
0.12458060229230839051 - 1.9743072850160517082e-1750j 8.21e-143, 2.21e-386j
6.7572303631139756775e-08 - 6.3253350621987050588e-1756j 4.45e-149, 1.2e-392j
0.0072921414973826526967 - 8.420280675839468626e-1752j 7.33e-145, 1.96e-388j
0.13337544348150416178 + 1.4402740126110539722e-1750j 2.83e-143, 7.58e-387j

Download

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