Rule: Q[8, 13, 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)
9.1164677113110924824 - 7.6642136400478265661e-1740j 3.27e-491, 3.27e-491j
-8.7712579998056290295 + 2.376579385010674008e-1763j 7.32e-491, 7.32e-491j
-10.254912975897125809 + 3.2406792597498342446e-1766j 8.4e-493, 8.4e-493j
-9.8538550857965168231 + 1.9237434386533410897e-1764j 3.49e-492, 3.49e-492j
8.4379969193709277074 + 3.6971867587304402001e-1761j 1.36e-490, 1.36e-490j
-10.688046295446472064 - 8.0455364767537114849e-1790j 1.27e-493, 1.27e-493j
7.1927545548832794661 + 2.1405412687724909303e-1785j 3.42e-490, 3.42e-490j
-11.169752561552635127 - 6.2821993484860385797e-1815j 1.26e-494, 1.26e-494j
9.4761485645558574451 - 1.5251817449693435465e-1809j 1.25e-491, 1.25e-491j
3.1824221178579781255 - 9.5759981916359433657e-1835j 1.23e-494, 1.23e-494j
0.94913656200810432963 - 2.2505795602849309117e-1844j 2.47e-504, 2.47e-504j
-9.1164677113110924824 - 1.6807095833888332133e-1830j 3.66e-491, 3.66e-491j
-1.3692600656263445545 + 1.1488889536089082147e-1841j 4.4e-502, 4.4e-502j
-6.3239078633044843298 - 4.4832222817411186173e-1828j 1.9e-490, 1.9e-490j
-7.8002643024201076658 - 6.5089802319562992371e-1828j 2.84e-490, 2.84e-490j
-9.4761485645558574451 - 6.1094423919789601153e-1833j 1.2e-491, 1.2e-491j
7.8002643024201076658 - 1.0394596739532253891e-1833j 2.81e-490, 2.81e-490j
9.8538550857965168231 + 1.8510014300261116074e-1858j 3.85e-492, 3.85e-492j
-3.5488890138692623718 - 5.3641378768926285581e-1875j 1.2e-491, 1.2e-491j
7.493217694514311019 + 2.1001973077154252268e-1879j 3.43e-490, 3.43e-490j
-12.81033274335329368 + 1.1067867070196256109e-1902j 3.54e-498, 3.54e-498j
-6.898119951913830952 - 5.558890922167821141e-1893j 3.36e-490, 3.36e-490j
-8.114811958218849941 - 5.5979124760343182256e-1894j 2.16e-490, 2.16e-490j
-1.7761512333605696549 - 1.7809546448402563652e-1904j 4.21e-500, 4.21e-500j
10.688046295446472064 + 5.3825729263324585994e-1894j 1.27e-493, 1.27e-493j
-7.493217694514311019 + 2.2855771059444727989e-1900j 3.41e-490, 3.41e-490j
3.90283294767709042 + 2.2198268239561760358e-1902j 4.33e-493, 4.33e-493j
5.2230373024948898096 + 2.7133542283825942344e-1901j 2.13e-491, 2.13e-491j
-3.1824221178579781255 + 6.1678464113917072907e-1918j 1.05e-494, 1.05e-494j
11.7413363213033006 + 5.9440741890345696411e-1914j 6.43e-496, 6.43e-496j
8.114811958218849941 - 2.2526815165844840851e-1918j 2.11e-490, 2.11e-490j
10.254912975897125809 + 5.6626017313797851059e-1933j 8.08e-493, 8.08e-493j
2.9306374202572440192 - 1.2896124646654026763e-1939j 1.79e-495, 1.79e-495j
-5.2230373024948898096 - 9.1446021859038506127e-1935j 2.24e-491, 2.24e-491j
4.9556459138464720181 - 9.5710374876467443782e-1935j 1.03e-491, 1.03e-491j
-1.5760077854370687303 + 8.112114836669699336e-1945j 4.53e-501, 4.53e-501j
5.766564510884910506 + 1.2864909319830276188e-1933j 7.67e-491, 7.67e-491j
1.7761512333605696549 - 1.3048097022293518364e-1956j 4.01e-500, 4.01e-500j
-1.9816567566958429259 - 3.1657513643733250084e-1955j 3.64e-499, 3.64e-499j
-5.4932398349220835953 + 3.4221078181708972375e-1946j 4.08e-491, 4.08e-491j
-2.5333214165462424981 + 1.2185841971244134975e-1952j 2.32e-496, 2.32e-496j
4.1661833588800450479 + 4.7729117127261316023e-1948j 8.45e-493, 8.45e-493j
8.7712579998056290295 - 5.1155814304493112466e-1946j 7.13e-491, 7.13e-491j
12.81033274335329368 + 5.5897798479977698575e-1959j 3.33e-498, 3.33e-498j
6.898119951913830952 - 1.4332410696613553495e-1950j 3.22e-490, 3.22e-490j
-2.6915799356368946606 - 2.278931894755496125e-1958j 5e-496, 5e-496j
6.0433353666994003258 - 3.0769473537316718805e-1951j 1.17e-490, 1.17e-490j
11.169752561552635127 - 5.9715778583017083796e-1959j 1.32e-494, 1.32e-494j
-11.7413363213033006 + 1.3559416070936505146e-1961j 6.32e-496, 6.32e-496j
4.427861101351666036 - 1.2256511312501301423e-1956j 1.87e-492, 1.87e-492j
2.4194104229642408382 - 1.1691040988795106292e-1961j 7.74e-497, 7.74e-497j
-2.199926525209156013 - 1.5492616509424362149e-1962j 4.48e-498, 4.48e-498j
-6.608682769024611343 - 2.781705997026570483e-1954j 2.55e-490, 2.55e-490j
-8.4379969193709277074 - 1.2380578674495083131e-1954j 1.45e-490, 1.45e-490j
2.199926525209156013 + 8.2785693473577590292e-1963j 4.27e-498, 4.27e-498j
6.3239078633044843298 - 5.0998854212050571412e-1953j 1.85e-490, 1.85e-490j
-0.38118699020732211685 - 5.5874869711212661229e-1977j 1.1e-507, 1.1e-507j
-3.5611468078266561951 + 3.1156226969594233088e-1960j 9.98e-492, 9.98e-492j
3.5488890138692623718 - 1.0079490202983818756e-1958j 1.22e-491, 1.22e-491j
-7.1927545548832794661 - 5.7732552684930180938e-1958j 3.43e-490, 3.43e-490j
1.5760077854370687303 + 2.6075380497749832147e-1970j 4.36e-501, 4.36e-501j
-4.6907336464704330151 + 4.0731051557007451567e-1960j 4.37e-492, 4.37e-492j
-2.4194104229642408382 + 5.0495945377114949845e-1966j 7.08e-497, 7.08e-497j
-3.5100667623092421974 - 9.9025638247571973946e-1961j 2.5e-492, 2.5e-492j
4.6907336464704330151 - 2.4102580862176929884e-1960j 4.77e-492, 4.77e-492j
2.5333214165462424981 - 4.9642687568741144216e-1967j 2.31e-496, 2.31e-496j
-5.766564510884910506 + 9.2482640259176407137e-1960j 7.05e-491, 7.05e-491j
-0.94913656200810432963 + 1.5313934880669841292e-1975j 2.55e-504, 2.55e-504j
6.608682769024611343 + 1.1040092123275644226e-1960j 2.61e-490, 2.61e-490j
2.6915799356368946606 - 2.767712898285422516e-1972j 5.57e-496, 5.57e-496j
1.3692600656263445545 - 9.2252366484334467892e-1979j 3.9e-502, 3.9e-502j
3.5100667623092421974 - 1.1808376755471346856e-1968j 2.43e-492, 2.43e-492j
1.9816567566958429259 - 2.7003605355961049954e-1976j 3.91e-499, 3.91e-499j
-4.1661833588800450479 - 1.8746053404462689341e-1968j 8.1e-493, 8.1e-493j
-4.9556459138464720181 + 4.4712017416425675996e-1967j 1.03e-491, 1.03e-491j
3.5611468078266561951 - 4.2129135606294416901e-1968j 9.75e-492, 9.75e-492j
0.56988506778275283872 + 4.5784713169982361214e-1984j 1.56e-506, 1.56e-506j
-6.0433353666994003258 + 4.9297222357785114301e-1970j 1.18e-490, 1.18e-490j
-0.75436086591777005941 + 7.9401438180764859884e-1985j 2.22e-505, 2.22e-505j
-4.427861101351666036 + 4.2388100545722322086e-1973j 1.86e-492, 1.86e-492j
1.1571937124467801947 - 7.9236315808181050091e-1984j 3.48e-503, 3.48e-503j
0.75436086591777005941 - 1.2829618754934770855e-1985j 2.04e-505, 2.04e-505j
5.4932398349220835953 + 1.4054932998453048143e-1976j 4.46e-491, 4.46e-491j
-2.8937466856038769018e-2029 - 7.5856639018727839024e-2029j 7.39e-2027, 7.39e-2027j
-2.9306374202572440192 - 1.0248789595695748784e-1989j 1.77e-495, 1.77e-495j
-3.90283294767709042 - 1.1728321080865479442e-1999j 3.94e-493, 3.94e-493j
0.38118699020732211685 + 2.7444797908035276065e-2014j 1.09e-507, 1.09e-507j
-1.1571937124467801947 - 1.0094447247506563615e-2010j 3.2e-503, 3.2e-503j
-0.18883826452039627711 + 9.6507299525696213226e-2016j 5.7e-509, 5.7e-509j
-0.56988506778275283872 - 2.5415148221265845973e-2014j 1.74e-506, 1.74e-506j
0.18883826452039627711 - 1.0035842167359603576e-2015j 5.7e-509, 5.7e-509j

Weights

Weight (ball center) Error (ball radius)
1.5984742601600465652e-37 + 1.2327416702335481317e-1775j 5.36e-151, 1.58e-395j
7.3966870972420065353e-35 - 2.062775100992377272e-1776j 8.33e-150, 2.45e-394j
4.9875706077648583449e-47 - 4.2289464468087516513e-1783j 3.28e-156, 9.67e-401j
1.4833896736779722397e-43 + 3.2375942386379129653e-1781j 8.88e-155, 2.61e-399j
2.2159462797307416628e-32 + 1.3286142737464294719e-1773j 1.26e-151, 3.7e-396j
6.2626654380448570454e-51 + 3.3887483648180945877e-1785j 2.03e-158, 5.99e-403j
5.7053125697283895457e-24 + 3.3158289863663124536e-1769j 7.87e-147, 2.32e-391j
1.9043426085367808344e-55 - 1.3426142490850025353e-1787j 8.61e-161, 2.54e-405j
2.0832730222085227479e-40 + 8.8438399426099583172e-1778j 1.06e-156, 3.12e-401j
5.837337488545223783e-06 + 1.4134594825517555757e-1756j 1.86e-119, 5.47e-364j
0.046417598202821368712 - 1.6151488294780842398e-1753j 2.9e-92, 8.55e-337j
1.5984742601600465652e-37 + 6.7191858820405409971e-1778j 3.24e-153, 9.55e-398j
0.018228811375282901276 - 4.8553172107531426176e-1754j 2.9e-92, 8.55e-337j
6.829333452437914386e-19 - 5.0863113201461695185e-1767j 8.86e-144, 2.61e-388j
6.5977978457554265051e-28 + 1.885385694992361433e-1772j 6.51e-150, 1.92e-394j
2.0832730222085227479e-40 - 1.7108726654284478389e-1779j 1.59e-154, 4.69e-399j
6.5977978457554265051e-28 + 2.4232245813420326327e-1771j 7.14e-153, 2.1e-397j
1.4833896736779722397e-43 - 8.3291645501629190796e-1780j 7.04e-162, 2.07e-406j
-1.8720944351508255072e-05 + 1.0671114440369464894e-1755j 2.54e-129, 7.49e-374j
7.060726100897277886e-26 - 2.9608862379666910574e-1770j 1.32e-151, 3.87e-396j
1.9109197984374941695e-71 - 1.0888353659842837109e-1795j 5.05e-171, 1.49e-415j
3.5581456138708428974e-22 - 4.7155402345243360614e-1769j 1.12e-148, 3.29e-393j
4.5329314091675165081e-30 - 1.0658151959135317032e-1773j 1.42e-152, 4.18e-397j
0.0048212057835012925548 - 1.9659562657554135709e-1754j 2.31e-112, 6.79e-357j
6.2626654380448570454e-51 - 4.2703887119548272711e-1784j 4.54e-168, 1.34e-412j
7.060726100897277886e-26 - 2.8936482046957514909e-1771j 8.98e-151, 2.65e-395j
3.6561750836061040384e-08 + 1.5738290780939527025e-1758j 4.3e-138, 1.27e-382j
2.1535769156553234679e-13 - 8.7386283258518940199e-1763j 1.31e-146, 3.87e-391j
5.837337488545223783e-06 + 6.8197480670720320327e-1757j 1.27e-131, 3.74e-376j
4.9275525527615783198e-61 - 1.2496842517182234504e-1789j 3.07e-173, 9.03e-418j
4.5329314091675165081e-30 - 1.833500148142177572e-1772j 2.03e-157, 5.99e-402j
4.9875706077648583449e-47 + 7.1958252254435075401e-1782j 3.77e-166, 1.11e-410j
2.5865777506831583001e-05 - 4.6956179486140398309e-1756j 1.5e-133, 4.42e-378j
2.1535769156553234679e-13 - 2.3726928664871648484e-1763j 4.06e-148, 1.2e-392j
3.242408597732937122e-12 + 5.8389438239732449485e-1762j 7.3e-147, 2.15e-391j
0.0095262990853900519797 + 3.1655711175963032301e-1754j 1.58e-119, 4.66e-364j
5.6109255503791229754e-16 - 1.7500646871517269263e-1764j 6.46e-151, 1.9e-395j
0.0048212057835012925548 - 2.9173690983338168126e-1754j 2.02e-124, 5.95e-369j
0.0023570011688318239757 + 1.1178980809053862759e-1754j 1.49e-125, 4.39e-370j
1.2033722313510501959e-14 + 3.1376268560167415068e-1764j 4.8e-150, 1.41e-394j
6.2959616107954618768e-05 - 4.8792741365628708643e-1755j 3.77e-132, 1.11e-376j
4.276197938092881697e-09 - 1.8078548722569670008e-1759j 7.33e-144, 2.16e-388j
7.3966870972420065353e-35 - 1.0688678209358188314e-1774j 3.59e-161, 1.06e-405j
1.9109197984374941695e-71 + 6.4633319276203849756e-1795j 5.72e-180, 1.69e-424j
3.5581456138708428974e-22 - 3.4042197462210675419e-1768j 6.11e-156, 1.8e-400j
9.1434764994142642798e-05 + 1.3876949246357633263e-1755j 2.02e-137, 5.95e-382j
2.1635139305739027353e-17 + 2.2903082697535219979e-1765j 1.73e-153, 5.08e-398j
1.9043426085367808344e-55 + 1.3264875740557797285e-1786j 1.58e-172, 4.66e-417j
4.9275525527615783198e-61 + 1.5726760878602456398e-1790j 2.32e-177, 6.82e-422j
4.5194069688478956561e-10 + 2.5529591933618364134e-1760j 1.02e-147, 2.99e-392j
0.00032551308215558341623 + 1.1038875509138984446e-1754j 8.09e-139, 2.38e-383j
0.00099561178066821983717 - 6.7048207236969132498e-1755j 5.78e-136, 1.7e-380j
1.7444835910623532727e-20 + 5.1294224984295266005e-1768j 1.45e-158, 4.28e-403j
2.2159462797307416628e-32 + 5.1350240377950220442e-1775j 5.73e-164, 1.69e-408j
0.00099561178066821983717 - 1.0969991004608908065e-1754j 2.13e-139, 6.27e-384j
6.829333452437914386e-19 - 2.8122783878216738437e-1766j 8.45e-156, 2.49e-400j
0.09371241347151927988 + 3.5280661188114823208e-1753j 1.97e-132, 5.8e-377j
1.3516382664683918831e-05 - 7.5394961918929877076e-1756j 1.45e-146, 4.27e-391j
-1.8720944351508255072e-05 + 2.4275089475538514423e-1755j 8.4e-147, 2.47e-391j
5.7053125697283895457e-24 + 3.9111024066176975377e-1770j 1.53e-160, 4.5e-405j
0.0095262990853900519797 + 4.4888232204468384759e-1754j 8.8e-138, 2.59e-382j
4.1393256039871535579e-11 - 1.2307292652547258386e-1761j 1.6e-154, 4.7e-399j
0.00032551308215558341623 + 6.4085265831630462339e-1755j 6.9e-142, 2.03e-386j
6.3700778889144457841e-06 - 3.3299140290846029929e-1756j 6.95e-147, 2.05e-391j
4.1393256039871535579e-11 - 3.8395724942633464301e-1761j 2.53e-152, 7.45e-397j
6.2959616107954618768e-05 - 8.6345513593050165432e-1755j 1.08e-144, 3.18e-389j
5.6109255503791229754e-16 - 3.9390812362142366756e-1765j 1.96e-158, 5.76e-403j
0.046417598202821368712 - 1.310547781092793922e-1753j 8.28e-141, 2.44e-385j
1.7444835910623532727e-20 + 3.2164217634818781244e-1767j 6.29e-159, 1.85e-403j
9.1434764994142642798e-05 + 2.5503897284505521654e-1755j 9.88e-146, 2.91e-390j
0.018228811375282901276 - 6.5715980351959108315e-1754j 1.67e-142, 4.91e-387j
6.3700778889144457841e-06 - 7.4995125509020830542e-1756j 2.06e-148, 6.07e-393j
0.0023570011688318239757 + 1.7388788747666403333e-1754j 3.24e-144, 9.55e-389j
4.276197938092881697e-09 - 6.7376577449091357827e-1760j 2.24e-155, 6.61e-400j
3.242408597732937122e-12 + 1.726450296245904157e-1762j 7.12e-158, 2.1e-402j
1.3516382664683918831e-05 - 1.7205635470918406551e-1755j 2.88e-149, 8.49e-394j
0.075377424472367553075 - 3.3167002024450321643e-1753j 1.37e-147, 4.03e-392j
2.1635139305739027353e-17 + 4.6428178431423799956e-1766j 3.66e-161, 1.08e-405j
0.059827815747741306282 + 2.1182222038424468244e-1753j 1.18e-147, 3.46e-392j
4.5194069688478956561e-10 + 8.8375153280111299816e-1761j 1.37e-156, 4.03e-401j
0.031321577216982561831 + 1.0014583935183299814e-1753j 7.11e-148, 2.09e-392j
0.059827815747741306282 + 2.500399558291611595e-1753j 6.4e-148, 1.88e-392j
1.2033722313510501959e-14 + 1.2651649942949947417e-1763j 4.93e-159, 1.45e-403j
0.10577556705207614823 + 4.2936723977184851685e-1753j 1.44e-149, 4.2e-394j
2.5865777506831583001e-05 - 2.4110602028067059078e-1756j 1.53e-152, 4.5e-397j
3.6561750836061040384e-08 + 6.302466014488967765e-1759j 3.54e-155, 1.05e-399j
0.09371241347151927988 + 3.8359790406785759934e-1753j 1.2e-149, 3.5e-394j
0.031321577216982561831 + 7.7585598976837805184e-1754j 1.41e-150, 4.16e-395j
0.10401364073964730837 - 4.0156929666867745595e-1753j 2.55e-150, 7.46e-395j
0.075377424472367553075 - 2.9264319636575782733e-1753j 1.69e-150, 5.07e-395j
0.10401364073964730837 - 4.1855737833572047114e-1753j 2.29e-150, 6.41e-395j

Download

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