Rule: Q[4, 5, 10, 52]

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)
9.2351960978161077819 - 7.2818519416969369209e-1883j 2.6e-497, 2.6e-497j
-9.7580011148152006031 - 1.0961470678295754036e-1880j 3.08e-498, 3.08e-498j
7.1818594339853961681 - 1.9903375861865965379e-1900j 7.31e-495, 7.31e-495j
-7.5503658529731142357 + 1.9835918951733216937e-1932j 3.9e-495, 3.9e-495j
9.7580011148152006031 - 2.5916330712402415631e-1959j 3.09e-498, 3.09e-498j
-7.1818594339853961681 - 3.3966501140239933315e-1969j 6.65e-495, 6.65e-495j
-6.4814160427385173755 - 6.1483643417289455018e-2000j 1.31e-494, 1.31e-494j
-7.9346211735839269698 - 2.4295707001123176464e-2018j 1.81e-495, 1.81e-495j
-9.2351960978161077819 - 2.4443658163124792855e-2023j 2.8e-497, 2.8e-497j
-5.4972571037117812749 - 1.6252912369936606299e-2020j 1.01e-494, 1.01e-494j
3.7457171898432240834 - 2.5826573653202436667e-2024j 9.05e-495, 9.05e-495j
5.18252874856594979 + 2.9252608937850333097e-2026j 8.23e-495, 8.23e-495j
-0.73395630342256598469 - 3.3043567732467012657e-2037j 8e-506, 8e-506j
1.6506801238857845559 + 6.9816044510124897501e-2033j 1.02e-501, 1.02e-501j
-10.389779340771663807 - 3.4211886673524146862e-2031j 1.24e-499, 1.24e-499j
-6.8262436647618208272 - 6.1579506390079930543e-2024j 1.01e-494, 1.01e-494j
3.4178874863247208453 - 4.9453934649326338704e-2040j 1.35e-496, 1.35e-496j
3.9569649052835232429 - 1.5037557228362813409e-2038j 3.1e-495, 3.1e-495j
-0.88116816034928950498 - 5.8774686655197964656e-2048j 4.58e-505, 4.58e-505j
-5.8180582610305896622 + 6.5765640217483025425e-2038j 1.33e-494, 1.33e-494j
4.8731302773482843181 - 1.5543894627581222948e-2050j 5.6e-495, 5.6e-495j
1.9141186905670222293 - 4.7216613690137993526e-2056j 5.72e-501, 5.72e-501j
6.4814160427385173755 + 1.8257003847296499129e-2048j 1.25e-494, 1.25e-494j
8.3386974596606001005 - 4.1896470709623042548e-2057j 6.46e-496, 6.46e-496j
4.2664980991948915808 - 1.3478731978022214077e-2060j 2.46e-495, 2.46e-495j
1.412013319838777997 + 5.8391817399799048045e-2068j 3.85e-502, 3.85e-502j
8.7687810610653725153 + 9.9385338430948264975e-2061j 1.56e-496, 1.56e-496j
-6.1457735607999565975 - 1.3900851215083701908e-2059j 1.45e-494, 1.45e-494j
10.389779340771663807 - 2.1045046743229700931e-2075j 1.3e-499, 1.3e-499j
4.5682735480200510579 + 6.2918366109329975097e-2071j 3.51e-495, 3.51e-495j
5.8180582610305896622 - 3.3015938033133371164e-2070j 1.28e-494, 1.28e-494j
2.6384291054842239697 + 3.3302828968425243597e-2077j 1.25e-498, 1.25e-498j
2.1711784782454809446 + 4.5384643897876789122e-2076j 4.27e-500, 4.27e-500j
-1.348911528920009526 - 7.5475664778738228365e-2078j 2.17e-502, 2.17e-502j
-1.9141186905670222293 - 4.2556239844380749561e-2076j 5.99e-501, 5.99e-501j
-3.4178874863247208453 + 1.1426099519733626495e-2069j 1.31e-496, 1.31e-496j
7.9346211735839269698 + 1.9293919571324964037e-2077j 1.74e-495, 1.74e-495j
-8.3386974596606001005 - 1.0629990649740000977e-2088j 6.5e-496, 6.5e-496j
-4.5682735480200510579 - 1.0653778280380776635e-2090j 3.79e-495, 3.79e-495j
-3.7457171898432240834 - 3.3095935207642823269e-2088j 9.66e-495, 9.66e-495j
-2.6384291054842239697 - 3.1732777346144047012e-2097j 1.2e-498, 1.2e-498j
-8.7687810610653725153 - 3.5246647247806263734e-2096j 1.71e-496, 1.71e-496j
-4.2664980991948915808 + 1.5998324347945826158e-2092j 2.32e-495, 2.32e-495j
1.1128991332067180798 + 5.8789654673275401467e-2104j 6.06e-504, 6.06e-504j
-3.9569649052835232429 - 1.7741484845383064717e-2092j 2.83e-495, 2.83e-495j
-1.1128991332067180798 - 1.3789035746077232215e-2104j 5.85e-504, 5.85e-504j
-3.7718846754027442829 + 9.7808071379026513454e-2094j 1.09e-494, 1.09e-494j
7.5503658529731142357 + 3.4010374045126344756e-2099j 4.2e-495, 4.2e-495j
5.4972571037117812749 + 4.7780566574368182858e-2098j 1.17e-494, 1.17e-494j
-2.4118974658184825981 - 3.455416009484526916e-2104j 2.88e-499, 2.88e-499j
-3.1393517534352283061 + 2.6042112844011008107e-2101j 2.28e-497, 2.28e-497j
2.4118974658184825981 - 9.3256021790162892064e-2104j 3.04e-499, 3.04e-499j
-2.8774454451159214784 - 2.6467582385382207267e-2102j 5.49e-498, 5.49e-498j
3.1393517534352283061 + 2.4246782855509560475e-2102j 2.42e-497, 2.42e-497j
0.73395630342256598469 + 1.7916190837489051984e-2111j 7.49e-506, 7.49e-506j
2.8774454451159214784 + 3.454550180458774033e-2103j 5.14e-498, 5.14e-498j
-1.6506801238857845559 + 4.0230305404607300619e-2107j 9.1e-502, 9.1e-502j
6.1457735607999565975 - 3.6849406560422269646e-2099j 1.39e-494, 1.39e-494j
0.26601423919855924139 - 5.6372125249303413407e-2114j 7.38e-509, 7.38e-509j
-0.52464762327529031788 - 1.4046796928577211214e-2112j 3.33e-507, 3.33e-507j
1.348911528920009526 - 3.3494793113494900459e-2107j 2.07e-502, 2.07e-502j
-4.8731302773482843181 + 2.4090497519739609118e-2098j 5.79e-495, 5.79e-495j
-2.1711784782454809446 - 2.5640030697271425126e-2113j 4.3e-500, 4.3e-500j
5.7772285283534193612e-2147 + 3.7173742521065266116e-2147j 4.88e-2145, 4.88e-2145j
6.8262436647618208272 - 1.2979372898420313483e-2107j 9.85e-495, 9.85e-495j
-5.18252874856594979 + 6.1282542882371334849e-2121j 8.2e-495, 8.2e-495j
-1.412013319838777997 + 1.1146547421218179834e-2134j 4.12e-502, 4.12e-502j
-0.26601423919855924139 - 1.4309593792157741859e-2139j 9.46e-509, 9.46e-509j
3.7718846754027442829 - 9.2380091757563951265e-2136j 1.12e-494, 1.12e-494j
0.88116816034928950498 - 1.8777895446891420144e-2149j 4.58e-505, 4.58e-505j
0.52464762327529031788 + 3.2551286403353584303e-2152j 3.96e-507, 3.96e-507j

Weights

Weight (ball center) Error (ball radius)
2.5180548764013246824e-38 + 1.8983290829803722015e-1919j 1.78e-182, 4.53e-429j
1.4094756249637425228e-42 - 1.6599408709190062804e-1921j 1.17e-184, 2.98e-431j
8.1134060042710289964e-24 - 2.1964676205286558444e-1912j 2.05e-175, 5.21e-422j
3.69946127254555951e-26 + 1.3897820277402572948e-1913j 2.9e-177, 7.37e-424j
1.4094756249637425228e-42 + 1.4866138663147602997e-1922j 7.34e-185, 1.87e-431j
8.1134060042710289964e-24 - 2.9126251355737180472e-1912j 4.57e-176, 1.16e-422j
1.0932885181018092349e-19 - 7.5933809336989176256e-1910j 5.6e-174, 1.43e-420j
1.0087928791434223339e-28 - 5.3694060605653672461e-1915j 2.59e-179, 6.6e-426j
2.5180548764013246824e-38 + 6.7187456212963566471e-1920j 1.61e-184, 4.11e-431j
1.3460037248051425046e-14 + 1.2115060311224787315e-1906j 3.4e-171, 8.65e-418j
4.5773643475386223874e-07 - 4.5095816061060059237e-1900j 2.68e-164, 6.81e-411j
3.8102797475380461485e-13 - 9.1944149953290627926e-1906j 6.15e-173, 1.57e-419j
0.050090394918588565055 + 2.9481490488019927281e-1896j 3.01e-144, 7.64e-391j
0.0097357793959429743524 - 3.1418821529090638307e-1897j 2.97e-144, 7.55e-391j
5.4173543249517075135e-48 - 2.6259048030779830055e-1925j 1.96e-189, 4.99e-436j
1.1436978036780765139e-21 + 5.0878568981348543923e-1911j 6.47e-176, 1.64e-422j
1.3642583291183958012e-06 + 1.7079286488302237348e-1900j 6.55e-163, 1.67e-409j
3.0594310103981836078e-08 - 1.9461309159033846091e-1901j 2.39e-166, 6.08e-413j
0.04917306807642742224 - 2.8218346285737805079e-1896j 3.61e-146, 9.19e-393j
3.6419150874536501388e-16 - 1.1485154666194403111e-1907j 2.68e-174, 6.82e-421j
8.4172278919241048675e-12 + 8.7236911942108015378e-1905j 3.53e-172, 8.96e-419j
0.0037867950081281475711 + 8.4491841510931412312e-1898j 3.76e-152, 9.56e-399j
1.0932885181018092349e-19 - 5.6905979060309243463e-1910j 1.84e-180, 4.68e-427j
1.48639137912620868e-31 + 1.4288622684150109494e-1916j 9.16e-188, 2.33e-434j
2.1142014088328598074e-09 + 8.8379235447199686631e-1903j 3.98e-170, 1.01e-416j
0.010493706916164923089 + 2.5945745709388004155e-1896j 4.76e-150, 1.21e-396j
1.0167322480442250457e-34 - 4.2670013502825913942e-1918j 3.82e-189, 9.7e-436j
7.3852412092372981504e-18 + 9.8946838785057369337e-1909j 1.26e-179, 3.21e-426j
5.4173543249517075135e-48 - 6.907523213000082195e-1926j 1.45e-195, 3.69e-442j
1.4771707281540927708e-10 - 8.3047015295759352912e-1904j 1.21e-172, 3.07e-419j
3.6419150874536501388e-16 - 8.713144509678916284e-1908j 3.97e-179, 1.01e-425j
0.00012202984872599692017 - 5.6733971139141585548e-1899j 4.74e-165, 1.2e-411j
0.0012674911563694356867 - 3.2354618763554648088e-1898j 7.82e-162, 1.99e-408j
0.013013396814348234999 - 3.3903555032143868609e-1896j 9.59e-158, 2.44e-404j
0.0037867950081281475711 + 9.356086616486261529e-1898j 2.14e-164, 5.45e-411j
1.3642583291183958012e-06 + 2.0416284860705442001e-1900j 3.4e-175, 8.65e-422j
1.0087928791434223339e-28 - 4.2999402726180843331e-1915j 6.1e-188, 1.55e-434j
1.48639137912620868e-31 + 1.624425020549142267e-1916j 8.6e-191, 2.19e-437j
1.4771707281540927708e-10 - 1.0467269350456181997e-1903j 3.19e-180, 8.1e-427j
4.5773643475386223874e-07 - 5.4764217841481443929e-1900j 1.68e-177, 4.28e-424j
0.00012202984872599692017 - 6.5225301483876619555e-1899j 1.21e-173, 3.08e-420j
1.0167322480442250457e-34 - 3.7304472097947810177e-1918j 8.57e-194, 2.18e-440j
2.1142014088328598074e-09 + 1.0993661200240744632e-1902j 3.56e-180, 9.04e-427j
0.04139851978490628089 + 1.7460480758982394598e-1896j 5.49e-166, 1.4e-412j
3.0594310103981836078e-08 - 2.3869282863602120268e-1901j 3.64e-179, 9.25e-426j
0.04139851978490628089 + 1.8532474846816232982e-1896j 6.23e-167, 1.58e-413j
-2.9712571350607762122e-07 + 5.1054792512245337527e-1900j 7.86e-178, 2e-424j
3.69946127254555951e-26 + 1.0677142864727292863e-1913j 3.06e-193, 7.77e-440j
1.3460037248051425046e-14 + 9.2787114166739103283e-1907j 5.03e-186, 1.28e-432j
0.00038724643756077727581 + 1.6028021979588644449e-1898j 2.79e-176, 7.1e-423j
8.0226508091657829681e-06 - 6.1774170311773925319e-1900j 1.21e-178, 3.09e-425j
0.00038724643756077727581 + 1.4104468827825313641e-1898j 9.26e-177, 2.35e-423j
3.5951675083150616292e-05 + 2.1243777488042012435e-1899j 5.78e-178, 1.47e-424j
8.0226508091657829681e-06 - 5.2391460013148829246e-1900j 5.15e-180, 1.31e-426j
0.050090394918588565055 + 2.834387814323747287e-1896j 1.5e-174, 3.82e-421j
3.5951675083150616292e-05 + 1.8255193583056112294e-1899j 3.76e-179, 9.55e-426j
0.0097357793959429743524 - 3.4312535801311484441e-1897j 1.32e-176, 3.36e-423j
7.3852412092372981504e-18 + 7.4501051833340140301e-1909j 1.71e-190, 4.34e-437j
0.13895510943616918829 + 1.1029546678012711139e-1896j 2.64e-175, 6.7e-422j
0.10627915972680244096 - 1.7399463186669173097e-1896j 5.83e-175, 1.48e-421j
0.013013396814348234999 - 3.1544070370122560091e-1896j 2.83e-175, 7.19e-422j
8.4172278919241048675e-12 + 1.1134551975279146881e-1904j 1.01e-186, 2.56e-433j
0.0012674911563694356867 - 3.6311567745184905919e-1898j 2.66e-179, 6.77e-426j
0.15050354083976451373 - 9.7937217023627339442e-1897j 8.65e-178, 2.19e-424j
1.1436978036780765139e-21 + 3.8115885592573316694e-1911j 1.25e-193, 3.19e-440j
3.8102797475380461485e-13 - 1.1875263065322737545e-1905j 7.92e-188, 2.01e-434j
0.010493706916164923089 + 2.7979971505297119714e-1896j 1.35e-177, 3.41e-424j
0.13895510943616918829 + 1.1188131515078159327e-1896j 2.55e-178, 6.44e-425j
-2.9712571350607762122e-07 + 4.1989179768116510369e-1900j 1.91e-182, 4.87e-429j
0.04917306807642742224 - 2.6916795680908494081e-1896j 7.52e-179, 1.99e-425j
0.10627915972680244096 - 1.6916597687913808578e-1896j 6.04e-179, 1.47e-425j

Download

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