Rule: Q[2, 3, 4, 20, 36]

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)
7.7747173970093172815 - 5.2232487643052642678e-1734j 1.69e-497, 1.69e-497j
6.9194417287647965301 - 4.3983447644483367369e-1754j 2.06e-496, 2.06e-496j
-8.2537940580172952401 - 2.4304601016742280102e-1770j 2.93e-498, 2.93e-498j
9.4398552828638770316 + 3.3598668280364537602e-1766j 1.45e-500, 1.45e-500j
8.2537940580172952401 + 4.1536539511634301568e-1770j 3.04e-498, 3.04e-498j
-7.7747173970093172815 + 2.0131624566316065765e-1786j 1.62e-497, 1.62e-497j
-5.0867759502606219565 + 5.8393809502190948628e-1782j 1.91e-495, 1.91e-495j
-1.0672470719421885588 - 9.4954777485216581816e-1794j 1.21e-503, 1.21e-503j
-4.4787590996579512123 + 1.2717360295662082968e-1783j 7.08e-496, 7.08e-496j
-6.9194417287647965301 + 5.0904771102242876105e-1786j 1.99e-496, 1.99e-496j
1.0672470719421885588 + 4.7720634952352490935e-1802j 1.28e-503, 1.28e-503j
8.7909178787116295882 - 1.3346396250304342867e-1792j 3.56e-499, 3.56e-499j
6.5274386966353144089 - 7.0716601313341585352e-1820j 5.15e-496, 5.15e-496j
-2.9321977529262635468 - 7.8854665023083781995e-1843j 2.8e-498, 2.8e-498j
5.8130758162857973667 - 1.4776657867809692824e-1844j 3.87e-495, 3.87e-495j
1.7320508075688772935 - 1.995434862139337792e-1867j 4.94e-502, 4.94e-502j
3.1695749797433954244 - 1.5203849253385954147e-1860j 1.04e-497, 1.04e-497j
-8.7909178787116295882 + 3.2607097426806097336e-1871j 3.37e-499, 3.37e-499j
7.3333390180724066356 + 2.7573424884765724613e-1870j 6.41e-497, 6.41e-497j
-3.4132612660636390352 + 1.1521440850659859355e-1879j 2.96e-497, 2.96e-497j
1.9846469105761808283 + 1.8066731400733268571e-1883j 4.23e-501, 4.23e-501j
4.7735853814474776058 - 6.243596465994741504e-1876j 1.15e-495, 1.15e-495j
5.6120018331855383582 - 2.1256202699337000359e-1880j 5.72e-495, 5.72e-495j
-6.5274386966353144089 - 1.2741145109232053847e-1889j 5.07e-496, 5.07e-496j
6.1553279759282458668 - 8.8305289338206201199e-1888j 1.35e-495, 1.35e-495j
-5.403367990235555017 + 8.6050748377256541645e-1895j 3.7e-495, 3.7e-495j
0.97778890935543307184 - 2.4405790178491382418e-1904j 2.87e-504, 2.87e-504j
5.0867759502606219565 - 4.5642683304940912297e-1894j 1.87e-495, 1.87e-495j
-4.7735853814474776058 - 2.2394270418177331315e-1904j 1.14e-495, 1.14e-495j
-0.97778890935543307184 + 4.1579510284634049984e-1915j 2.79e-504, 2.79e-504j
3.4132612660636390352 + 1.4568717315329421516e-1903j 2.97e-497, 2.97e-497j
2.2060595696653970513 - 1.213704227146547368e-1908j 2.86e-500, 2.86e-500j
1.4585997653268697444 - 2.015532395487555679e-1911j 6.81e-503, 6.81e-503j
3.6745625916955208506 - 2.8109389213178191138e-1903j 7e-497, 7e-497j
-7.3333390180724066356 + 3.5400242907062562706e-1909j 6.6e-497, 6.6e-497j
-3.9409498244546404992 + 1.0500773334378403103e-1909j 1.78e-496, 1.78e-496j
-3.1695749797433954244 - 1.5144425869337029588e-1910j 9.21e-498, 9.21e-498j
-1.9846469105761808283 - 2.5508423578579649695e-1914j 4.37e-501, 4.37e-501j
-1.7320508075688772935 - 1.4318283852462956235e-1915j 4.89e-502, 4.89e-502j
-1.4585997653268697444 - 6.6443952443104665537e-1916j 6.11e-503, 6.11e-503j
-6.1553279759282458668 - 3.9963968642777670586e-1907j 1.3e-495, 1.3e-495j
2.9321977529262635468 + 2.4610181141332530309e-1909j 2.87e-498, 2.87e-498j
-5.8130758162857973667 - 1.6681104047817702355e-1906j 3.75e-495, 3.75e-495j
-5.6120018331855383582 + 3.8477747956839231951e-1909j 5.22e-495, 5.22e-495j
2.4321650054069606588 + 1.7223132876399906903e-1912j 1.46e-499, 1.46e-499j
-9.4398552828638770316 - 3.1689170709908096763e-1915j 1.38e-500, 1.38e-500j
-2.2060595696653970513 + 3.7115426861660298138e-1914j 2.6e-500, 2.6e-500j
-2.6822224032999497583 - 1.9754762815411700268e-1914j 6.22e-499, 6.22e-499j
0.7071067811865475244 + 6.4853037551093435034e-1920j 3.14e-506, 3.14e-506j
-2.4321650054069606588 + 3.9244242033122471216e-1913j 1.49e-499, 1.49e-499j
-0.7071067811865475244 - 6.828952598744799508e-1920j 3.62e-506, 3.62e-506j
-0.48932189980227080554 - 4.0286797762276941045e-1921j 1.63e-507, 1.63e-507j
5.403367990235555017 + 1.1302814663261114975e-1907j 3.95e-495, 3.95e-495j
1.1530591875902305495 - 2.6485673576234684738e-1927j 1.63e-503, 1.63e-503j
2.6822224032999497583 - 2.529591987468941354e-1920j 6.09e-499, 6.09e-499j
-4.2051169778104238937 + 8.8154053399348845628e-1920j 3.86e-496, 3.86e-496j
4.4787590996579512123 - 1.9180603773329593763e-1917j 6.8e-496, 6.8e-496j
-1.1530591875902305495 + 2.6377302813426612842e-1949j 1.67e-503, 1.67e-503j
3.9409498244546404992 + 4.1367303392214561672e-1940j 1.72e-496, 1.72e-496j
0.48932189980227080554 + 8.7361945970361696469e-1970j 1.91e-507, 1.91e-507j
4.2051169778104238937 - 2.5286147265294519052e-1967j 3.95e-496, 3.95e-496j
-3.6745625916955208506 + 4.3084192972358830602e-1992j 7.52e-497, 7.52e-497j
-0.25557983664008304578 - 6.7059157978658653191e-2005j 6.34e-509, 6.34e-509j
4.0161974140942281778e-2011 - 5.1642521396648552386e-2012j 2.63e-2009, 2.63e-2009j
0.25557983664008304578 - 3.515838717343854553e-2005j 6.34e-509, 6.34e-509j

Weights

Weight (ball center) Error (ball radius)
1.4481183634929767557e-27 + 7.4859091186833429157e-1760j 1.75e-181, 1.13e-428j
3.6519874348291534837e-22 + 3.3732079917648351229e-1757j 1.35e-178, 8.71e-426j
7.3603418574096342365e-31 - 4.0437592772296962566e-1764j 1.54e-185, 9.99e-433j
8.432827314206056366e-40 + 1.6659569834175517988e-1768j 7.19e-188, 4.65e-435j
7.3603418574096342365e-31 + 1.3529242221917999963e-1762j 1.69e-183, 1.09e-430j
1.4481183634929767557e-27 + 4.8644098984176799031e-1762j 2.18e-184, 1.41e-431j
1.0423907123613784622e-12 + 2.3111684089922831916e-1751j 1.93e-174, 1.25e-421j
-0.073200588444762362007 + 1.6635804989522473383e-1741j 1.52e-136, 9.81e-384j
3.1085825014692554228e-10 + 1.4675388116708414645e-1749j 1.72e-171, 1.11e-418j
3.6519874348291534837e-22 + 1.9633806157876619531e-1758j 4.18e-182, 2.7e-429j
-0.073200588444762362007 + 2.1929757345335966276e-1741j 6.28e-139, 4.06e-386j
8.9392661446314115108e-35 - 2.6229101660787383875e-1765j 2.29e-187, 1.48e-434j
6.7516642565407995381e-20 - 9.8053286798945821503e-1756j 1.02e-180, 6.63e-428j
2.5300969212650281968e-05 + 1.6102367491339069136e-1745j 9.62e-165, 6.22e-412j
3.6710790858699592261e-16 - 9.5390360518587467118e-1753j 3.96e-179, 2.56e-426j
0.0074661324707476301389 - 3.0074441314892233067e-1743j 1.44e-154, 9.32e-402j
5.7704837605635123587e-06 - 1.1792453417599892882e-1745j 8.82e-168, 5.7e-415j
8.9392661446314115108e-35 + 1.6089950852277869711e-1766j 8.77e-192, 5.67e-439j
1.061261835169289604e-24 - 1.2451194465219628239e-1758j 1.75e-183, 1.13e-430j
1.2466905065528616792e-06 + 1.2443667823195106234e-1746j 1.37e-170, 8.87e-418j
0.0025938397870877718438 + 1.5425945851853026402e-1743j 3.09e-159, 2e-406j
2.1869748671109498733e-11 - 7.8170935071083451371e-1750j 7.72e-177, 4.99e-424j
1.4231456708811175129e-15 + 6.3061000867922377772e-1752j 3.89e-179, 2.52e-426j
6.7516642565407995381e-20 - 8.5511425917337160826e-1757j 2.55e-186, 1.65e-433j
7.1573669907618034224e-18 + 2.9060515611540689163e-1754j 8.58e-181, 5.55e-428j
3.5514196027550519433e-14 - 3.8263936955445804259e-1752j 2.05e-182, 1.32e-429j
0.09376170607961831055 - 1.5108869884742992388e-1741j 8.08e-155, 5.22e-402j
1.0423907123613784622e-12 + 1.1058677320754077274e-1750j 2.21e-178, 1.43e-425j
2.1869748671109498733e-11 - 1.8695858720511836755e-1750j 7.47e-180, 4.83e-427j
0.09376170607961831055 - 1.1733085877491723781e-1741j 4.59e-157, 2.97e-404j
1.2466905065528616792e-06 + 3.1920415089922710528e-1746j 2.29e-173, 1.48e-420j
0.00093237165065885001592 - 7.8993807844892032526e-1744j 1.89e-167, 1.22e-414j
0.018820115119190878848 + 8.0230854566817084148e-1743j 1.74e-162, 1.12e-409j
2.0553630139078507698e-07 - 7.2434876093108047042e-1747j 9.92e-175, 6.41e-422j
1.061261835169289604e-24 - 3.63758770678190229e-1760j 1.6e-190, 1.03e-437j
2.6878306462980935634e-08 + 5.143709327053777391e-1748j 4.31e-179, 2.79e-426j
5.7704837605635123587e-06 - 4.9620318580281656511e-1746j 6.75e-176, 4.37e-423j
0.0025938397870877718438 + 9.1519602083823942498e-1744j 2.83e-171, 1.83e-418j
0.0074661324707476301389 - 1.9115835983259852161e-1743j 9.71e-170, 6.28e-417j
0.018820115119190878848 + 5.4882498480774359204e-1743j 4.24e-168, 2.74e-415j
7.1573669907618034224e-18 + 3.3783300981859082508e-1755j 6.05e-188, 3.92e-435j
2.5300969212650281968e-05 + 3.5602681065735607851e-1745j 7.69e-177, 4.98e-424j
3.6710790858699592261e-16 - 1.3771308898812003788e-1753j 5.8e-187, 3.75e-434j
1.4231456708811175129e-15 + 1.0187933705200701434e-1752j 3.78e-186, 2.44e-433j
0.0003665525169643960686 + 3.1265703924618804853e-1744j 4.67e-177, 3.02e-424j
8.432827314206056366e-40 - 1.6114533545964129056e-1769j 1.11e-202, 7.2e-450j
0.00093237165065885001592 - 4.4073671602514241527e-1744j 2.27e-177, 1.47e-424j
0.00010771034869659025062 - 5.0466547766941200542e-1745j 1.96e-179, 1.27e-426j
0.07820808116538036688 + 5.1934168706202532286e-1742j 1.11e-174, 7.18e-422j
0.0003665525169643960686 + 1.636529693318111292e-1744j 1.32e-178, 8.54e-426j
0.07820808116538036688 + 4.3274945856041259008e-1742j 3.99e-175, 2.58e-422j
0.097171129035622605164 - 3.9720303968916825755e-1742j 1.19e-175, 7.67e-423j
3.5514196027550519433e-14 - 2.1264071292515635376e-1751j 9.05e-190, 5.86e-437j
0.06947255274491585849 - 1.0113462988490938485e-1741j 7.75e-177, 5.01e-424j
0.00010771034869659025062 - 1.0362811403451993251e-1744j 9.67e-182, 6.26e-429j
3.1367069028368482143e-09 - 9.5256461991603417282e-1749j 3.18e-186, 2.06e-433j
3.1085825014692554228e-10 + 5.4559101525059881801e-1749j 1.7e-188, 1.1e-435j
0.06947255274491585849 - 7.5010720293916196894e-1742j 2.87e-179, 1.85e-426j
2.6878306462980935634e-08 + 1.5718737669729434871e-1747j 2.44e-187, 1.58e-434j
0.097171129035622605164 - 4.5055913986587139965e-1742j 1.91e-181, 1.23e-428j
3.1367069028368482143e-09 - 3.196875010584026469e-1748j 4.04e-188, 2.61e-435j
2.0553630139078507698e-07 - 2.5939989726730656848e-1747j 5.97e-187, 3.87e-434j
0.13115821318126250898 + 3.361754301334256435e-1742j 7.59e-182, 4.9e-429j
0.14621926063202874062 - 3.1224272816504869541e-1742j 2.51e-182, 1.63e-429j
0.13115821318126250898 + 3.5902902493098947807e-1742j 2.36e-182, 1.5e-429j

Download

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