Rule: Q[2, 12, 99]

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.

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)
-13.291678122217428247 + 1.0430470430751532708e-1217j 9.42e-492, 9.42e-492j
10.649923891311542986 - 4.3760902054104175291e-1213j 4.97e-486, 4.97e-486j
12.394866207667683755 - 4.4076757288362987023e-1217j 2.24e-489, 2.24e-489j
-13.867100798845139356 - 1.2251091558614091568e-1219j 1.61e-493, 1.61e-493j
11.297763849353941687 - 1.1108978616191026977e-1214j 4.71e-487, 4.71e-487j
3.270676901126319117 - 8.6037911843542422395e-1220j 1.92e-492, 1.92e-492j
11.642829000352034173 + 2.075421325164869117e-1215j 1.06e-487, 1.06e-487j
-1.7042623277902273645 + 4.0613888490334153878e-1226j 4.25e-499, 4.25e-499j
-12.394866207667683755 - 8.9850065441046160767e-1215j 2.46e-489, 2.46e-489j
4.5642364512675538347 - 2.041977869912018986e-1216j 4.39e-489, 4.39e-489j
1.9229065254485963272 + 1.3543928821979873406e-1224j 3.42e-497, 3.42e-497j
-12.817058720680949012 + 4.1653789935502301337e-1217j 1.95e-490, 1.95e-490j
-3.6848675290705506763 + 6.6711157970388457776e-1218j 2.42e-491, 2.42e-491j
10.96767511977916515 - 1.2039005423243508807e-1213j 1.78e-486, 1.78e-486j
-11.642829000352034173 - 1.6667352581408600723e-1210j 1.1e-487, 1.1e-487j
-7.1272678886056208204 - 1.1415184025065933775e-1218j 6.95e-485, 6.95e-485j
8.6517871770078006672 - 7.3246724945856176206e-1230j 2.02e-484, 2.02e-484j
13.291678122217428247 - 3.5859781846330855644e-1239j 9.29e-492, 9.29e-492j
-6.6430627780420702338 - 2.264959443970312005e-1253j 2.16e-485, 2.16e-485j
-10.044124766446977614 - 1.7166313046279937281e-1297j 2.96e-485, 2.96e-485j
12.817058720680949012 + 6.1351595083018238115e-1332j 1.99e-490, 1.99e-490j
1.7042623277902273645 + 3.1922730026019380649e-1375j 3.91e-499, 3.91e-499j
-8.6517871770078006672 + 5.5174650749490319439e-1369j 2.03e-484, 2.03e-484j
-8.1295946753394140804 - 8.0347519774385109431e-1409j 1.99e-484, 1.99e-484j
5.2416494814534959293 + 4.9830720167181425018e-1442j 1.46e-487, 1.46e-487j
-10.96767511977916515 - 4.9385778915365538307e-1437j 1.71e-486, 1.71e-486j
1.4919998411007081827 - 9.7813433050874586833e-1469j 1.5e-500, 1.5e-500j
4.788497263259211366 + 2.6032183395236159611e-1455j 1.58e-488, 1.58e-488j
-5.470625658334337373 + 6.4048003626272720679e-1454j 3.92e-487, 3.92e-487j
-0.7071067811865475244 + 1.2287763377426136652e-1472j 1.03e-504, 1.03e-504j
10.044124766446977614 + 3.107961069720508969e-1451j 2.79e-485, 2.79e-485j
-11.297763849353941687 - 2.7204742609267100928e-1456j 4.76e-487, 4.76e-487j
2.341737087843858481 - 9.0263575001279006026e-1477j 3.54e-496, 3.54e-496j
6.1681273139855524196 - 4.3947807883283109984e-1468j 5.5e-486, 5.5e-486j
-12.006628040564441552 - 1.1058550797430112366e-1465j 1.75e-488, 1.75e-488j
-8.9193185409141515898 - 1.2432613868848420997e-1475j 1.69e-484, 1.69e-484j
12.006628040564441552 + 1.7999669592978787923e-1493j 1.76e-488, 1.76e-488j
0.86120969988140481794 - 2.0062508724585924934e-1508j 5.19e-504, 5.19e-504j
5.470625658334337373 + 9.4645405722433534645e-1492j 3.99e-487, 3.99e-487j
-2.1305320498116726639 - 8.0353962477979679006e-1502j 5.09e-497, 5.09e-497j
-0.6176389073448524302 + 5.5957062693331689541e-1510j 2.12e-505, 2.12e-505j
-9.46955474595453802 - 7.4489237259335026208e-1488j 8.69e-485, 8.69e-485j
8.9193185409141515898 + 3.3356972092453871816e-1502j 1.72e-484, 1.72e-484j
-10.342567753551082331 + 2.8266043996323551939e-1503j 1.27e-485, 1.27e-485j
8.1295946753394140804 - 1.0200297111148393605e-1511j 1.91e-484, 1.91e-484j
-2.7518151176497469031 - 1.2138979263779301484e-1539j 2.16e-494, 2.16e-494j
-7.3732833477367061676 + 2.8127908261887878141e-1529j 9.69e-485, 9.69e-485j
-7.8741960794744415291 + 2.6002507726140158784e-1562j 1.72e-484, 1.72e-484j
1.2798739543845792198 - 3.6999648138876459022e-1598j 8.84e-502, 8.84e-502j
9.7534318039550299323 + 1.2495043534429957429e-1579j 5.11e-485, 5.11e-485j
-10.649923891311542986 - 5.0055610652547584062e-1598j 4.93e-486, 4.93e-486j
-1.8942430499246252602 + 4.2061774065585347651e-1622j 2.8e-497, 2.8e-497j
-5.7012987006323959989 + 9.7521810683269851168e-1610j 9.68e-487, 9.68e-487j
5.7012987006323959989 - 4.0415714917937443597e-1620j 1.05e-486, 1.05e-486j
-8.3886773560127461124 - 1.5077536391984901268e-1617j 2.09e-484, 2.09e-484j
6.4045148095820873127 + 2.0085945029255753536e-1635j 1.11e-485, 1.11e-485j
-1.4919998411007081827 - 9.8276328765383065756e-1650j 1.43e-500, 1.43e-500j
6.8839239277021086734 - 2.2951012117335542066e-1634j 3.99e-485, 3.99e-485j
-3.4728186067144971606 - 2.3485547330055662271e-1641j 6.41e-492, 6.41e-492j
0.42058914410350368836 - 2.7153402667731729819e-1656j 3.96e-507, 3.96e-507j
-1.0686290085475260915 - 1.3695587054803232028e-1652j 5.37e-503, 5.37e-503j
5.0142923660595300628 - 8.0095415957024106648e-1639j 4.61e-488, 4.61e-488j
7.8741960794744415291 - 1.4765156611238322852e-1634j 1.75e-484, 1.75e-484j
13.867100798845139356 + 1.3977752009492562427e-1643j 1.6e-493, 1.6e-493j
2.1305320498116726639 - 1.3236694500896891891e-1646j 4.86e-497, 4.86e-497j
7.1272678886056208204 - 1.8915483352525795195e-1634j 6.73e-485, 6.73e-485j
-7.6221808078986387466 - 1.6724838856989013511e-1634j 1.45e-484, 1.45e-484j
-0.42058914410350368836 + 3.7449649686883686943e-1668j 4.09e-507, 4.09e-507j
-3.0920473364687008144 - 1.1527060216628253538e-1653j 5.97e-493, 5.97e-493j
3.0920473364687008144 + 8.9418416703177075618e-1655j 5.64e-493, 5.64e-493j
4.3415290458743119398 - 3.1693716699493264866e-1650j 1.3e-489, 1.3e-489j
3.4728186067144971606 + 1.2038589280732175581e-1652j 6.49e-492, 6.49e-492j
-2.341737087843858481 + 3.2313653537058820508e-1657j 3.25e-496, 3.25e-496j
-1.9229065254485963272 + 2.1357078103776032774e-1658j 3.52e-497, 3.52e-497j
8.3886773560127461124 - 1.8539350443885310839e-1643j 2.09e-484, 2.09e-484j
1.8942430499246252602 - 4.141149939965117365e-1659j 2.52e-497, 2.52e-497j
6.6430627780420702338 + 2.0093430324362240112e-1647j 2.25e-485, 2.25e-485j
-5.0142923660595300628 + 1.723478901258405855e-1647j 4.58e-488, 4.58e-488j
-1.2798739543845792198 - 4.2086787731014106412e-1663j 8.81e-502, 8.81e-502j
-6.4045148095820873127 + 7.0993718058377592531e-1647j 1.17e-485, 1.17e-485j
-9.7534318039550299323 - 1.9000245569463691717e-1664j 5.54e-485, 5.54e-485j
4.1204787410992218738 - 2.3856168361794043342e-1685j 3.53e-490, 3.53e-490j
-2.9326831063505245306 - 5.988471422542951286e-1690j 1.42e-493, 1.42e-493j
-3.270676901126319117 - 7.8116998172941111552e-1688j 1.79e-492, 1.79e-492j
-2.5504966051126501465 - 1.5001715295725009345e-1690j 2.78e-495, 2.78e-495j
9.46955474595453802 + 2.7032376563992878224e-1678j 9.04e-485, 9.04e-485j
0.6176389073448524302 + 4.991509903015676974e-1703j 2.34e-505, 2.34e-505j
-5.9337629391838743968 - 4.1008742366581451824e-1683j 2.48e-486, 2.48e-486j
-4.5642364512675538347 - 8.8245682051131772086e-1688j 4.28e-489, 4.28e-489j
-4.788497263259211366 - 3.7851421810885816091e-1687j 1.42e-488, 1.42e-488j
10.342567753551082331 + 1.1084664797266490435e-1681j 1.33e-485, 1.33e-485j
7.6221808078986387466 - 1.7691349930284103065e-1682j 1.36e-484, 1.36e-484j
2.9326831063505245306 - 8.6292056429020117299e-1696j 1.45e-493, 1.45e-493j
5.9337629391838743968 - 3.662574752825261516e-1688j 2.31e-486, 2.31e-486j
-5.2416494814534959293 + 1.4009967477179938057e-1688j 1.39e-487, 1.39e-487j
3.6848675290705506763 - 1.7003236928254646392e-1693j 2.45e-491, 2.45e-491j
2.7518151176497469031 + 1.0036361682101274926e-1696j 2.19e-494, 2.19e-494j
0.7071067811865475244 - 8.2943313395802865985e-1707j 9.87e-505, 9.87e-505j
1.0686290085475260915 + 1.8457695099750331445e-1705j 5.14e-503, 5.14e-503j
-4.1204787410992218738 + 1.9773014764142139349e-1692j 3.55e-490, 3.55e-490j
-4.3415290458743119398 - 1.5238867167145115401e-1691j 1.28e-489, 1.28e-489j
-9.1917289808527198717 + 1.3905318023673074046e-1685j 1.34e-484, 1.34e-484j
2.5504966051126501465 - 6.1472896627098373299e-1704j 2.71e-495, 2.71e-495j
7.3732833477367061676 - 1.5189068957321094438e-1693j 9.9e-485, 9.9e-485j
-6.1681273139855524196 - 7.9682767480132772916e-1694j 5.5e-486, 5.5e-486j
-3.9013626594135512669 - 3.8020104070336331669e-1699j 9.27e-491, 9.27e-491j
-0.21096799267853511108 - 3.0756109348837102523e-1717j 9.05e-509, 9.05e-509j
3.9013626594135512669 + 3.314293520983238196e-1700j 8.95e-491, 8.95e-491j
0.21096799267853511108 - 2.9042065796201507699e-1717j 8.11e-509, 8.11e-509j
9.1917289808527198717 - 4.7237187223706049215e-1694j 1.29e-484, 1.29e-484j
-0.86120969988140481794 - 7.8465654059342909926e-1713j 4.97e-504, 4.97e-504j
3.1436403431120983124e-1763 + 1.2115311198627266504e-1763j 3.81e-1761, 3.81e-1761j
-6.8839239277021086734 - 3.6051294226195690369e-1692j 3.93e-485, 3.93e-485j

Weights

Weight (ball center) Error (ball radius)
5.4247187912902739973e-78 - 9.3002227379780371553e-1265j 1.1e-136, 1.47e-376j
9.7252177995998663251e-51 - 7.1972557003588142136e-1250j 3.1e-126, 4.15e-366j
4.3157555321024234765e-68 + 4.0941358723973761247e-1259j 4.83e-134, 6.46e-374j
1.152572390921136427e-84 + 3.1374334023807245667e-1268j 2.82e-140, 3.77e-380j
7.0148567320418322051e-57 - 3.6606507436827157279e-1253j 1.4e-129, 1.87e-369j
2.4651902085645104207e-06 + 8.2486161194334537369e-1223j 7.94e-75, 1.06e-314j
2.6856289078390043406e-60 + 5.5251352852446572495e-1255j 4.83e-131, 6.46e-371j
0.0065511193994139872287 - 1.8715029286262836384e-1220j 2.34e-46, 3.13e-286j
4.3157555321024234765e-68 - 1.3829365247489907595e-1259j 1.23e-136, 1.65e-376j
1.1307198771544756299e-10 + 1.4741645301794891344e-1225j 4.88e-92, 6.52e-332j
0.0024256042514334116113 - 1.1483726737236973719e-1219j 8.16e-54, 1.09e-293j
1.1331635445894332387e-72 + 5.5492001647857636005e-1262j 6.23e-138, 8.32e-378j
1.5359841820187303362e-07 + 7.4515179226532951544e-1224j 3.87e-85, 5.17e-325j
1.0474309195328699659e-53 + 1.8288436927347450716e-1251j 8.18e-130, 1.09e-369j
2.6856289078390043406e-60 - 1.7176774616826840844e-1255j 9.38e-135, 1.25e-374j
1.1986595205801535673e-23 - 9.8410839819096146202e-1236j 3.96e-115, 5.29e-355j
4.6414393827101190727e-34 + 1.0005628520292659631e-1240j 1.71e-122, 2.29e-362j
5.4247187912902739973e-78 + 2.5317750808690551935e-1264j 2.47e-141, 3.3e-381j
9.2366476221170600273e-21 - 3.963835938327139795e-1234j 1.03e-112, 1.37e-352j
2.5515245120269167678e-45 + 1.5170800633876971055e-1247j 2.16e-130, 2.88e-370j
1.1331635445894332387e-72 - 1.576375929823132815e-1261j 2.07e-139, 2.77e-379j
0.0065511193994139872287 - 2.9158134273757816023e-1220j 4.17e-59, 5.56e-299j
4.6414393827101190727e-34 - 1.8058338825699733946e-1241j 1.34e-124, 1.78e-364j
2.8775159521723216479e-30 - 2.1450825787215718412e-1239j 4.19e-122, 5.6e-362j
1.5047441242262853947e-13 + 4.1220549777296976335e-1228j 1.28e-106, 1.7e-346j
1.0474309195328699659e-53 - 5.2105530499803817959e-1252j 2.09e-134, 2.79e-374j
0.012930783488577142642 + 2.4747548419984684334e-1220j 2.12e-59, 2.84e-299j
1.3976994816955684958e-11 + 2.4451369865752851669e-1226j 4.24e-103, 5.66e-343j
1.304186683098907885e-14 + 3.04945091851762276e-1231j 1.2e-109, 1.6e-349j
0.024315621777564023614 + 2.1302622599237171583e-1219j 8.85e-61, 1.18e-300j
2.5515245120269167678e-45 - 6.1598776953721637245e-1247j 3.58e-132, 4.78e-372j
7.0148567320418322051e-57 + 1.0902702203667190262e-1253j 1.56e-135, 2.09e-375j
0.00049318913150143758233 - 2.9662641917579284097e-1221j 1.67e-79, 2.23e-319j
3.9816996386826311319e-18 + 2.6435442580778192607e-1231j 2.22e-115, 2.96e-355j
5.2211033761108997522e-64 + 1.9169420072895601316e-1257j 3.27e-138, 4.37e-378j
4.291813962361794855e-36 + 1.4140459345511612534e-1242j 1.11e-127, 1.49e-367j
5.2211033761108997522e-64 - 5.9137030026431186721e-1257j 2.99e-140, 4e-380j
0.054108929681399088604 - 1.121394567677890688e-1219j 1.56e-68, 2.09e-308j
1.304186683098907885e-14 - 6.5412759325327612848e-1229j 1.74e-111, 2.33e-351j
0.0012752832013586843945 + 5.1901252419281230179e-1221j 7.95e-83, 1.06e-322j
0.064465161965901055518 - 2.0048238274190468586e-1219j 8.96e-69, 1.2e-308j
1.8007990987902722621e-40 + 6.0770963857366182199e-1245j 2.08e-130, 2.78e-370j
4.291813962361794855e-36 - 7.2935628170047198578e-1242j 1.2e-130, 1.61e-370j
5.977138124863732536e-48 - 5.9739296018899242156e-1249j 1.62e-133, 2.16e-373j
2.8775159521723216479e-30 + 1.3994047158478295985e-1238j 4.14e-128, 5.54e-368j
5.6327580430773746082e-05 - 4.2361380689351483096e-1222j 1.04e-94, 1.39e-334j
3.422203482315907211e-25 + 1.3636642860762040644e-1236j 2.65e-123, 3.54e-363j
1.6909543591594501963e-28 + 2.0190084626740939133e-1238j 3.51e-125, 4.69e-365j
0.023229387168099414623 - 3.0698812614865317923e-1220j 3.92e-75, 5.24e-315j
7.8584890146934420856e-43 + 1.4014230111580967785e-1245j 1.23e-135, 1.64e-375j
9.7252177995998663251e-51 + 1.957946738654217252e-1250j 3.52e-135, 4.71e-375j
0.00064116180192205658516 + 7.7051698963669741442e-1220j 2.48e-87, 3.31e-327j
9.9865322762021011802e-16 - 1.6753570010872049646e-1231j 2.83e-118, 3.78e-358j
9.9865322762021011802e-16 + 1.0572166689919983225e-1229j 9e-119, 1.2e-358j
4.0444678875990994771e-32 + 2.0704821898553558391e-1240j 3.93e-127, 5.25e-367j
2.0567287472604459071e-19 - 3.9797580930881679602e-1232j 2.04e-123, 2.72e-363j
0.012930783488577142642 + 1.6718333672078290427e-1220j 7.29e-86, 9.73e-326j
3.5879520923767196466e-22 - 7.8302276762297456072e-1234j 1.27e-126, 1.69e-366j
6.8054288890002637769e-07 - 2.2879432460649047645e-1223j 5.12e-109, 6.83e-349j
0.098200377400454711697 + 9.7498727057447441922e-1220j 9.7e-81, 1.3e-320j
0.037877302437174253753 + 3.6709477823782981491e-1220j 1.59e-80, 2.12e-320j
1.5385201021744668613e-12 - 2.8015988856338554958e-1227j 1.84e-116, 2.45e-356j
1.6909543591594501963e-28 - 1.4474746754337842357e-1237j 2.01e-131, 2.68e-371j
1.152572390921136427e-84 - 8.1492718128023280771e-1268j 1.87e-157, 2.5e-397j
0.0012752832013586843945 + 8.8642981716849282373e-1221j 7.97e-99, 1.06e-338j
1.1986595205801535673e-23 + 1.0100754117814303209e-1234j 3.28e-128, 4.38e-368j
8.2908755097844773048e-27 - 1.734074092115320987e-1237j 1.93e-129, 2.58e-369j
0.098200377400454711697 + 8.7084442995868698843e-1220j 8.27e-87, 1.11e-326j
6.4808383917788296621e-06 - 1.4048575875159428061e-1222j 6.88e-110, 9.2e-350j
6.4808383917788296621e-06 - 2.4143350411093451545e-1222j 4.09e-109, 5.46e-349j
8.1589158642126323778e-10 - 4.2536268099527368318e-1225j 3.18e-116, 4.25e-356j
6.8054288890002637769e-07 - 2.3033498645631654251e-1223j 6.26e-112, 8.37e-352j
0.00049318913150143758233 - 1.6752620706005877862e-1221j 1.8e-105, 2.41e-345j
0.0024256042514334116113 - 7.0149574511320028995e-1220j 3.87e-100, 5.17e-340j
4.0444678875990994771e-32 - 1.2401646685061155495e-1239j 1.7e-134, 2.27e-374j
0.00064116180192205658516 + 1.2535080887425480485e-1219j 1.96e-100, 2.62e-340j
9.2366476221170600273e-21 + 5.7286911707001306984e-1233j 9.2e-127, 1.23e-366j
1.5385201021744668613e-12 - 2.8895746334091575654e-1229j 8.14e-126, 1.09e-365j
0.023229387168099414623 - 2.1872647329637640157e-1220j 1.93e-98, 2.57e-338j
2.0567287472604459071e-19 + 2.1977002001662266092e-1233j 2.94e-130, 3.93e-370j
7.8584890146934420856e-43 - 3.2699146581400787336e-1246j 4.74e-141, 6.33e-381j
5.2546660540474275415e-09 + 8.6035404943436701037e-1225j 1.22e-118, 1.63e-358j
1.720162335736315155e-05 + 2.6438427738708277549e-1222j 1.05e-113, 1.41e-353j
2.4651902085645104207e-06 + 5.4473761949970231085e-1223j 3.57e-116, 4.77e-356j
0.00017415074878258403594 + 7.5551095610920789391e-1222j 1.57e-111, 2.1e-351j
1.8007990987902722621e-40 - 2.7587222956041866748e-1244j 8.56e-143, 1.14e-382j
0.064465161965901055518 - 2.3659362273544162276e-1219j 6.25e-104, 8.35e-344j
6.7329672313234469307e-17 + 4.790216590712044958e-1232j 1.03e-129, 1.38e-369j
1.1307198771544756299e-10 - 1.9108519873303005503e-1227j 8.13e-126, 1.09e-365j
1.3976994816955684958e-11 + 2.5474332671946824709e-1228j 2.02e-126, 2.7e-366j
5.977138124863732536e-48 + 2.3049497562356299233e-1248j 1.47e-147, 1.96e-387j
8.2908755097844773048e-27 + 1.3810621545220799889e-1236j 4.76e-137, 6.36e-377j
1.720162335736315155e-05 + 4.749611359801730428e-1222j 1.48e-120, 1.98e-360j
6.7329672313234469307e-17 - 1.6931218756497494065e-1230j 1.7e-130, 2.27e-370j
1.5047441242262853947e-13 + 1.8522823515116532278e-1230j 4.66e-130, 6.22e-370j
1.5359841820187303362e-07 + 6.9893966932102866906e-1224j 6.49e-124, 8.66e-364j
5.6327580430773746082e-05 - 7.7412366141186167633e-1222j 1.54e-120, 2.06e-360j
0.024315621777564023614 + 2.5745319421809069701e-1219j 8.52e-114, 1.14e-353j
0.037877302437174253753 + 4.8794038777594416116e-1220j 2.88e-115, 3.85e-355j
5.2546660540474275415e-09 - 1.0346812091960285446e-1225j 1.39e-127, 1.85e-367j
8.1589158642126323778e-10 + 1.3708349874136411964e-1226j 3.38e-128, 4.53e-368j
3.1489842530170298407e-38 - 9.8653474133756458129e-1244j 1.26e-145, 1.69e-385j
0.00017415074878258403594 + 1.371101585874851673e-1221j 2.64e-122, 3.49e-362j
3.422203482315907211e-25 - 1.222668986436623196e-1235j 1.38e-138, 1.84e-378j
3.9816996386826311319e-18 - 1.0976024404819538796e-1232j 4.2e-135, 5.56e-375j
3.0171567626770179889e-08 + 1.0012403912258183414e-1224j 9.29e-128, 1.14e-367j
0.11367557067125949528 - 6.3871582698873915279e-1220j 6.88e-122, 7.93e-362j
3.0171567626770179889e-08 - 2.3041734538072994581e-1224j 4.58e-128, 5.71e-368j
0.11367557067125949528 - 6.7598921034038167255e-1220j 3.75e-122, 4.42e-362j
3.1489842530170298407e-38 + 4.762631278266915971e-1243j 1.11e-146, 1.44e-386j
0.054108929681399088604 - 8.9079050920387820828e-1220j 1.42e-122, 1.61e-362j
0.11910602226117142873 + 5.9958089171729097532e-1220j 8.45e-123, 7.38e-363j
3.5879520923767196466e-22 + 6.5220697778005109551e-1235j 8.69e-138, 1.24e-377j

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