Rule: Q[9, 14, 70]

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.

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)
10.144851564813520399 + 8.4116113664788316539e-1807j 2.2e-492, 2.2e-492j
-11.492153436947915616 - 2.7593588898714458244e-1812j 3.56e-495, 3.56e-495j
-10.144851564813520399 - 6.0226221179584937965e-1808j 2.38e-492, 2.38e-492j
-10.995146304963250562 - 2.6742329446975736621e-1811j 5.03e-494, 5.03e-494j
10.995146304963250562 - 3.4805039114436853003e-1811j 4.82e-494, 4.82e-494j
12.093831213796972245 - 2.1585026329547095008e-1817j 9.68e-497, 9.68e-497j
-8.7162998304770656728 - 1.1051709214102244259e-1807j 1.67e-490, 1.67e-490j
-9.7624439594635621305 + 7.8973934805439919136e-1820j 9.96e-492, 9.96e-492j
-2.6602671868269422397 - 4.4117007879556407467e-1833j 4.05e-495, 4.05e-495j
6.5983721082924902021 - 1.0747716042230176621e-1826j 5.3e-490, 5.3e-490j
3.1909932017815276072 - 8.9668063213003448034e-1839j 1.77e-494, 1.77e-494j
9.0514958982091444915 - 1.2986836645802092651e-1833j 7.58e-491, 7.58e-491j
10.552452782106823589 + 2.4731393791256479881e-1842j 4.27e-493, 4.27e-493j
-1.4685532892166679317 + 1.3898155017688770493e-1852j 1.95e-501, 1.95e-501j
-12.093831213796972245 - 1.0648815194910085602e-1847j 9.5e-497, 9.5e-497j
2.5968217484054892385 + 7.1069930896916212859e-1846j 3.84e-495, 3.84e-495j
8.7162998304770656728 + 2.9207353518061644924e-1839j 1.69e-490, 1.69e-490j
4.9672299093212664525 - 1.4260329163029160104e-1847j 2.52e-491, 2.52e-491j
-2.4988722345708622911 - 8.335901991773225922e-1853j 8.62e-496, 8.62e-496j
6.8830640582154683782 - 2.2685844218533668305e-1845j 7.09e-490, 7.09e-490j
1.4685532892166679317 + 2.2539834163564074812e-1863j 2.37e-501, 2.37e-501j
1.0727832560223829795 - 8.0247091574014966121e-1865j 3.93e-503, 3.93e-503j
9.7624439594635621305 - 4.732001733100609586e-1853j 9.7e-492, 9.7e-492j
-7.1725614723899632097 - 6.5306320702514547742e-1850j 7.3e-490, 7.3e-490j
-9.3992951326168870574 - 3.5034524593630838706e-1853j 2.98e-491, 2.98e-491j
6.3179968528404335228 + 5.5016905777951253384e-1851j 4.05e-490, 4.05e-490j
1.2414356460307046507 - 2.0243050261935738278e-1869j 2.09e-502, 2.09e-502j
-7.7683458217209946946 - 1.8450501682263667568e-1853j 6.77e-490, 6.77e-490j
-5.4987187806868916499 + 2.7158110978187476054e-1855j 9.5e-491, 9.5e-491j
-4.4436725456953199306 - 4.2330353906522239687e-1857j 5.74e-492, 5.74e-492j
-8.3916841550486189081 - 4.617777518198026645e-1854j 3.09e-490, 3.09e-490j
6.0415110433901436676 + 3.4406470481298044173e-1855j 2.69e-490, 2.69e-490j
0.72355101875283757332 + 2.5792049535802854423e-1874j 3.29e-505, 3.29e-505j
-6.8830640582154683782 + 1.5772231818933607003e-1857j 6.58e-490, 6.58e-490j
4.7047852943829738402 + 2.7175807792347415674e-1859j 1.12e-491, 1.12e-491j
-3.8910872313751438324 - 2.936168676409306382e-1862j 4.95e-492, 4.95e-492j
-9.0514958982091444915 - 1.014886017985340402e-1860j 7.76e-491, 7.76e-491j
2.9378789405121769728 + 1.0114598479479525501e-1863j 3.99e-495, 3.99e-495j
2.4988722345708622911 + 1.8372089469254737802e-1864j 9.67e-496, 9.67e-496j
-8.0761041678249019231 - 2.7896418417815841894e-1859j 5.05e-490, 5.05e-490j
4.4436725456953199306 - 4.7187182198346628505e-1861j 5.44e-492, 5.44e-492j
-5.2317324539479656178 - 3.7669361843751071113e-1860j 4.76e-491, 4.76e-491j
-3.4470054364527072683 + 8.8970477216184049037e-1863j 1.05e-493, 1.05e-493j
-10.552452782106823589 - 5.5213130237703000125e-1863j 4.2e-493, 4.2e-493j
5.7685342565264502053 + 1.1317385033695678482e-1857j 1.74e-490, 1.74e-490j
7.7683458217209946946 + 2.5518656102362366088e-1866j 6.78e-490, 6.78e-490j
-4.181733396241829206 - 3.1996526715648170515e-1892j 3e-492, 3e-492j
8.3916841550486189081 - 1.0382861333047328035e-1888j 3.16e-490, 3.16e-490j
11.492153436947915616 + 4.3087088228194543036e-1905j 3.53e-495, 3.53e-495j
9.3992951326168870574 - 7.4547857921637100317e-1908j 2.94e-491, 2.94e-491j
4.181733396241829206 - 1.1771209117216916776e-1916j 3.21e-492, 3.21e-492j
-2.9378789405121769728 + 2.3407974142612102203e-1919j 3.71e-495, 3.71e-495j
-3.7832466850882959409 + 2.6067952522273674355e-1915j 1.28e-491, 1.28e-491j
-5.7685342565264502053 + 8.5394691964172927269e-1915j 1.6e-490, 1.6e-490j
8.0761041678249019231 + 1.2577302493654971018e-1918j 4.79e-490, 4.79e-490j
2.6602671868269422397 + 1.2569718116895009015e-1939j 3.92e-495, 3.92e-495j
-7.4674322041351292319 - 1.2400945199823437944e-1933j 8.04e-490, 8.04e-490j
5.4987187806868916499 - 1.0696457911827329055e-1943j 9.01e-491, 9.01e-491j
3.7832466850882959409 - 6.603565656045265381e-1958j 1.32e-491, 1.32e-491j
0.93588957168758885766 - 4.2182107880846121887e-1984j 7.23e-504, 7.23e-504j
-2.1300894857898550963 - 7.1439232587305797158e-1978j 9.24e-498, 9.24e-498j
7.4674322041351292319 + 1.7152735597155364804e-1970j 7.81e-490, 7.81e-490j
-6.3179968528404335228 - 5.4083318681415370545e-1977j 4.27e-490, 4.27e-490j
-3.7548726437168948007 - 7.4556130872195335081e-1986j 9.22e-492, 9.22e-492j
3.4470054364527072683 - 1.1652426286406058235e-1988j 9.38e-494, 9.38e-494j
3.7548726437168948007 - 2.8159968889011920964e-1986j 9.74e-492, 9.74e-492j
-6.0415110433901436676 + 1.37395685214118207e-1984j 2.6e-490, 2.6e-490j
-1.2414356460307046507 + 2.4699373789341969799e-2003j 1.9e-502, 1.9e-502j
-0.45470735727117678391 + 1.1676548264597007686e-2007j 9.17e-507, 9.17e-507j
1.9366468705568828024 + 1.1728317196720506194e-1999j 6.17e-499, 6.17e-499j
2.2665805845318431118 + 7.3098573911263255392e-1999j 4.95e-497, 4.95e-497j
5.2317324539479656178 + 4.6155795011242027394e-1993j 4.87e-491, 4.87e-491j
-0.93588957168758885766 - 2.9475178634642888654e-2010j 7.14e-504, 7.14e-504j
-1.7042991202053013319 - 3.8071496251012936703e-2006j 3.23e-500, 3.23e-500j
-2.2665805845318431118 + 9.680321700203107042e-2003j 4.61e-497, 4.61e-497j
-3.1909932017815276072 + 1.0586360716260271193e-2000j 1.72e-494, 1.72e-494j
-2.5968217484054892385 + 2.1005395089388364754e-2002j 3.97e-495, 3.97e-495j
-4.7047852943829738402 + 1.263979329883344371e-1995j 1.15e-491, 1.15e-491j
-0.72355101875283757332 - 5.7742032691843683835e-2012j 3.4e-505, 3.4e-505j
-0.54431479141505793416 + 3.0553775290919765581e-2012j 4.29e-506, 4.29e-506j
0.54431479141505793416 - 3.7878145656215994207e-2012j 4.36e-506, 4.36e-506j
2.1300894857898550963 + 1.9826621343700356881e-2004j 9.53e-498, 9.53e-498j
0.23552806840077888258 + 5.5050486084944676675e-2015j 1.4e-508, 1.4e-508j
-1.0727832560223829795 + 2.4742740787812336261e-2009j 3.95e-503, 3.95e-503j
-4.9672299093212664525 - 8.8519210284895709152e-1997j 2.54e-491, 2.54e-491j
-1.9366468705568828024 - 1.5005961591650560031e-2018j 6.59e-499, 6.59e-499j
1.7042991202053013319 - 1.1072164739001125084e-2019j 3.01e-500, 3.01e-500j
-6.5983721082924902021 - 1.81865067099356575e-2010j 5.57e-490, 5.57e-490j
-1.3845971936794899435e-2060 - 2.1340335690789756283e-2061j 1.3e-2058, 1.3e-2058j
-0.23552806840077888258 + 1.531014816704933484e-2050j 1.56e-508, 1.56e-508j
7.1725614723899632097 + 2.1585606305043064103e-2047j 7.04e-490, 7.04e-490j
0.45470735727117678391 - 3.2402902065419362454e-2067j 1.11e-506, 1.11e-506j
3.8910872313751438324 + 1.1590988647967281181e-2067j 4.94e-492, 4.94e-492j

Weights

Weight (ball center) Error (ball radius)
4.4663419851439853475e-46 - 3.1225371198498229079e-1849j 3.56e-160, 3e-404j
1.3281573178624352176e-58 - 2.8496216931047352407e-1855j 1.88e-165, 1.58e-409j
4.4663419851439853475e-46 + 4.0665599728197781865e-1848j 4.97e-161, 4.18e-405j
8.2401250798149581712e-54 + 1.4124379465946464546e-1852j 7.13e-164, 6e-408j
8.2401250798149581712e-54 - 1.6304742542398513757e-1853j 6.5e-166, 5.46e-410j
1.1851430718320109193e-64 - 2.0387789529632815428e-1859j 5.15e-170, 4.33e-414j
1.8810207957616223117e-34 - 2.0824703609269752774e-1840j 4.34e-157, 3.65e-401j
8.5387400595067808408e-43 - 3.7324166033484948249e-1846j 2.29e-160, 1.93e-404j
0.00021959477865959266639 + 3.7761896102336653783e-1820j 9.46e-116, 7.96e-360j
1.9671706352676016765e-20 + 3.5379192388240875634e-1834j 1.82e-149, 1.53e-393j
5.4097408151934870102e-06 + 9.2782639963336012571e-1823j 5.02e-124, 4.22e-368j
5.0437870382628133466e-37 + 3.9573109683581248271e-1844j 1.59e-160, 1.33e-404j
1.040461637881476014e-49 + 2.9563107701700852565e-1851j 1.46e-165, 1.23e-409j
0.015282751638641613113 - 2.0849321500261728322e-1819j 3.68e-100, 3.09e-344j
1.1851430718320109193e-64 + 1.2570219702352811397e-1858j 3.41e-172, 2.87e-416j
-0.00024142248714021624382 - 4.4369546861428715671e-1820j 4.42e-120, 3.71e-364j
1.8810207957616223117e-34 - 1.1934529974995103143e-1842j 1.13e-159, 9.54e-404j
2.8609759952221238923e-12 + 1.892566114347851255e-1828j 1.08e-142, 9.12e-387j
0.00038153797579059000784 + 6.7738522663570245305e-1820j 5.46e-121, 4.59e-365j
4.3046188020560284082e-22 - 3.1004357704993564773e-1835j 1.3e-152, 1.1e-396j
0.015282751638641613113 - 1.4837327277883990585e-1819j 1.35e-105, 1.14e-349j
0.020859433103418951618 - 1.0878898266892983263e-1818j 1.16e-96, 9.74e-341j
8.5387400595067808408e-43 + 2.1196931079438707865e-1847j 2.71e-163, 2.28e-407j
7.4881209576910258897e-24 + 2.5389214524193755509e-1835j 8.01e-158, 6.73e-402j
8.5718155391195797355e-40 + 2.7721402052317244504e-1844j 4.14e-165, 3.48e-409j
7.2488352625997592206e-19 - 3.7049579203123594594e-1833j 1.16e-151, 9.73e-396j
0.025813368479080459094 + 4.4259528312891181442e-1819j 4.25e-105, 3.57e-349j
1.061975801341849037e-27 + 1.9444149349226124391e-1837j 2.08e-160, 1.75e-404j
1.1190040441435464691e-14 + 1.2459101198227143475e-1829j 8.54e-152, 7.18e-396j
3.9103563343030619462e-10 + 4.0830568036256843758e-1826j 7.36e-146, 6.19e-390j
4.7122235864444675752e-32 + 1.5605453541867349772e-1839j 1.09e-162, 9.2e-407j
2.1804800923448486561e-17 + 3.5971150615923988796e-1832j 6.88e-154, 5.79e-398j
0.073968650706209636148 - 1.8567152959277274517e-1818j 1.35e-108, 1.14e-352j
4.3046188020560284082e-22 - 2.6374201952245163446e-1834j 4.48e-158, 3.77e-402j
3.5972249153377908244e-11 - 1.5410287375625097806e-1827j 2.74e-148, 2.31e-392j
6.7572303631139756775e-08 + 1.6591170975493648619e-1823j 4.76e-144, 4e-388j
5.0437870382628133466e-37 - 2.095442297524827671e-1842j 4.35e-165, 3.66e-409j
2.558739190523962558e-05 - 5.5132188135655141981e-1822j 6.6e-137, 5.55e-381j
0.00038153797579059000784 + 3.7555024231504587242e-1820j 8.87e-133, 7.46e-377j
8.2923904346241244338e-30 - 1.6270044004811773422e-1838j 4.77e-162, 4.01e-406j
3.9103563343030619462e-10 + 1.3258132545266471959e-1826j 2.47e-148, 2.07e-392j
1.9440383210947928485e-13 - 9.349390779216099356e-1829j 5.45e-153, 4.59e-397j
1.0158176248344026887e-06 - 5.4992987380247127657e-1823j 1.22e-143, 1.03e-387j
1.040461637881476014e-49 - 3.1119254257883646155e-1850j 5.89e-172, 4.95e-416j
5.4120448377515413944e-16 - 3.2719967770627087376e-1831j 9.2e-156, 7.73e-400j
1.061975801341849037e-27 + 1.1186414861280334523e-1838j 1.02e-165, 8.62e-410j
3.7960891777646511173e-09 - 3.9064510453602860824e-1825j 9.41e-150, 7.91e-394j
4.7122235864444675752e-32 + 2.962934181484901858e-1841j 5.36e-168, 4.51e-412j
1.3281573178624352176e-58 + 3.9104847017028955973e-1856j 3.67e-181, 3.09e-425j
8.5718155391195797355e-40 - 1.0468075371844431614e-1845j 1.09e-171, 9.17e-416j
3.7960891777646511173e-09 - 1.3735573472384803985e-1825j 4.48e-152, 3.76e-396j
2.558739190523962558e-05 - 1.1118457674672196739e-1821j 1.89e-146, 1.59e-390j
-4.0895473362467138482e-07 - 1.4981497069446807479e-1822j 2.28e-150, 1.92e-394j
5.4120448377515413944e-16 - 1.6074787240657963605e-1830j 1.25e-160, 1.05e-404j
8.2923904346241244338e-30 - 6.2060708139595414202e-1840j 8.83e-168, 7.43e-412j
0.00021959477865959266639 + 2.0102975065995057835e-1820j 4.35e-145, 3.66e-389j
1.0184554827970860208e-25 - 2.2849447047006823057e-1836j 2.85e-166, 2.39e-410j
1.1190040441435464691e-14 + 2.8206509706149270886e-1830j 8.91e-159, 7.49e-403j
-4.0895473362467138482e-07 - 5.9131953448120777023e-1823j 7.44e-153, 6.25e-397j
0.043885237003783643783 + 1.4130900872761505897e-1818j 5.67e-138, 4.77e-382j
0.00087593849822056169631 + 9.8910469213186335492e-1820j 9.2e-147, 7.74e-391j
1.0184554827970860208e-25 - 1.7639329065573734881e-1837j 1.48e-166, 1.25e-410j
7.2488352625997592206e-19 - 2.3219643498550538187e-1832j 1.18e-164, 9.96e-409j
5.1489039558267227642e-07 + 1.4873533293387491788e-1822j 1.17e-152, 9.83e-397j
1.0158176248344026887e-06 - 2.3825855115745533921e-1823j 1.5e-152, 1.26e-396j
5.1489039558267227642e-07 + 5.917775864349882925e-1823j 6.27e-153, 5.28e-397j
2.1804800923448486561e-17 + 1.9842203613915319507e-1831j 5.53e-164, 4.65e-408j
0.025813368479080459094 + 5.89591233874865061e-1819j 2.58e-145, 2.17e-389j
0.081446399303909061323 - 4.0020537834230607289e-1818j 3.98e-144, 3.35e-388j
0.0029789097937157422895 - 5.7528527065925633026e-1820j 1.67e-148, 1.41e-392j
0.00057078811242056419325 - 4.4356346436676891791e-1820j 3.54e-149, 2.97e-393j
1.9440383210947928485e-13 - 2.3361083913719521012e-1829j 1.59e-159, 1.33e-403j
0.043885237003783643783 + 1.7530060663548624072e-1818j 2.6e-146, 2.19e-390j
0.0072921414973826526967 + 1.1098968728765962307e-1819j 9.19e-150, 7.73e-394j
0.00057078811242056419325 - 7.5527745778568602673e-1820j 1.13e-151, 9.48e-396j
5.4097408151934870102e-06 + 1.9993403662039354567e-1822j 2.4e-155, 2.02e-399j
-0.00024142248714021624382 - 8.2020857655592578688e-1820j 2.23e-152, 1.88e-396j
3.5972249153377908244e-11 - 5.154991704796396933e-1827j 7.68e-162, 6.46e-406j
0.073968650706209636148 - 2.1928390521939262078e-1818j 7.3e-150, 6.14e-394j
0.035366156878371625593 + 4.4918477890402407312e-1818j 8.49e-150, 7.14e-394j
0.035366156878371625593 + 3.9638611382552740362e-1818j 1.89e-150, 1.59e-394j
0.00087593849822056169631 + 6.006420459877232933e-1820j 3.9e-153, 3.28e-397j
0.12458060229230839051 + 1.3698931708770314983e-1818j 4.81e-151, 4.05e-395j
0.020859433103418951618 - 1.3932289529260957963e-1818j 5.4e-151, 4.54e-395j
2.8609759952221238923e-12 + 6.9065005125380954205e-1828j 4.77e-163, 4.01e-407j
0.0029789097937157422895 - 9.0390907270126425127e-1820j 8.9e-154, 7.53e-398j
0.0072921414973826526967 + 7.46878653121960912e-1820j 4.36e-154, 3.67e-398j
1.9671706352676016765e-20 + 2.5575617920503061783e-1833j 4.28e-169, 3.6e-413j
0.13337544348150416178 - 1.0872130897334025897e-1818j 1.94e-153, 1.69e-397j
0.12458060229230839051 + 1.4459744216581700743e-1818j 1.95e-153, 1.72e-397j
7.4881209576910258897e-24 + 2.4676217204962917384e-1836j 4.13e-172, 3.45e-416j
0.081446399303909061323 - 3.6052415735021253131e-1818j 1.58e-153, 1.48e-397j
6.7572303631139756775e-08 + 6.3506125633353073788e-1824j 1.29e-159, 1.06e-403j

Download

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