Rule: Q[1, 60]

Type

This rule is of Hermite (probabilists') 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)
3.2276822527149105572 + 9.6177662939329270416e-1457j 5.25e-501, 5.25e-501j
14.498533915900149317 + 2.4431789928473293694e-1451j 1.18e-499, 1.18e-499j
5.3110308195370260446 - 4.6701857484831436217e-1455j 1.63e-497, 1.63e-497j
1.6051847101182256355 - 8.6857382586134161688e-1462j 7.35e-505, 7.35e-505j
4.887411810748714214 + 8.0287451822927503639e-1456j 4.81e-498, 4.81e-498j
2.8194188542255728953 - 5.3144500408485106369e-1460j 5.64e-502, 5.64e-502j
2.008475226640472094 + 2.0173301877261747698e-1462j 1e-503, 1e-503j
2.4131208142506848327 - 6.0670424899909006085e-1461j 8.95e-503, 8.95e-503j
3.6382430676068060947 + 7.4128958994326954529e-1459j 3.26e-500, 3.26e-500j
1.2029642303011723284 - 1.4387485180717532205e-1464j 5.9e-506, 5.9e-506j
4.0514567191649028933 - 8.2907207251735901786e-1458j 2.48e-499, 2.48e-499j
0.8015382630317265855 + 4.514940362440041925e-1465j 3.6e-507, 3.6e-507j
5.7390739549506931965 - 1.2183659834893482786e-1454j 6.93e-497, 6.93e-497j
6.1721127891630710448 - 1.6718757711264786201e-1454j 1.67e-496, 1.67e-496j
4.4677069572407988504 - 1.2416748893063627853e-1458j 1.02e-498, 1.02e-498j
-8.4387669441217875807 - 9.5961357754376475965e-1458j 3.85e-495, 3.85e-495j
12.188457192776551964 + 4.9616125629865564351e-1474j 1.25e-496, 1.25e-496j
-14.498533915900149317 - 8.1742518384776547258e-1473j 1.18e-499, 1.18e-499j
7.0558612422325789793 - 6.4730401613715127856e-1480j 8.89e-496, 8.89e-496j
6.6107947002797749877 + 1.723502352487067228e-1480j 4.1e-496, 4.1e-496j
-10.448964909729461348 + 7.5230520158687099477e-1479j 1.94e-495, 1.94e-495j
-12.853564295912951536 + 1.17542934467468303e-1491j 2.58e-497, 2.58e-497j
-2.4131208142506848327 + 1.409952841812516457e-1505j 9.25e-503, 9.25e-503j
-11.574803203521677055 + 1.9364306442062369228e-1497j 5.36e-496, 5.36e-496j
-13.598659156615787863 + 6.2658838584034394529e-1506j 2.86e-498, 2.86e-498j
-7.0558612422325789793 + 8.9752464567463049299e-1513j 7.62e-496, 7.62e-496j
-5.7390739549506931965 - 8.3535467886921432536e-1524j 6.23e-497, 6.23e-497j
-2.8194188542255728953 + 2.0466363144251138286e-1536j 6.03e-502, 6.03e-502j
8.919721841212938333 + 1.442907942882625075e-1527j 3.73e-495, 3.73e-495j
-12.188457192776551964 - 1.1685172083877795639e-1535j 1.35e-496, 1.35e-496j
9.413418928509502288 - 2.9834129626596943603e-1547j 3.33e-495, 3.33e-495j
-1.6051847101182256355 + 1.1629408147209529933e-1563j 6.88e-505, 6.88e-505j
12.853564295912951536 - 2.4360450123207026994e-1552j 2.49e-497, 2.49e-497j
-8.919721841212938333 - 6.3955079427305118273e-1566j 4.25e-495, 4.25e-495j
-3.2276822527149105572 + 2.6580939697855567107e-1586j 5.4e-501, 5.4e-501j
8.4387669441217875807 - 4.6000912794312965139e-1580j 3.88e-495, 3.88e-495j
-4.0514567191649028933 + 1.2590878905468105798e-1584j 2.51e-499, 2.51e-499j
-5.3110308195370260446 - 1.2728603273705535764e-1580j 1.57e-497, 1.57e-497j
9.9221626372550859863 - 3.1579650041217777542e-1583j 2.81e-495, 2.81e-495j
10.997909441340786088 + 7.5232244610964425956e-1585j 1.03e-495, 1.03e-495j
-4.887411810748714214 + 2.6379844442555672979e-1584j 4.78e-498, 4.78e-498j
-1.2029642303011723284 - 1.6362987842728027609e-1605j 5.29e-506, 5.29e-506j
-6.1721127891630710448 + 2.3188405159476342386e-1594j 1.77e-496, 1.77e-496j
7.9687387811758625868 + 2.1984253246518959824e-1617j 1.89e-495, 1.89e-495j
-10.997909441340786088 - 4.045088662820024426e-1668j 8.66e-496, 8.66e-496j
-7.9687387811758625868 - 1.3158956025016142944e-1721j 1.96e-495, 1.96e-495j
-0.8015382630317265855 + 1.3068772001266971283e-1755j 3.6e-507, 3.6e-507j
13.598659156615787863 - 3.0460266944376876098e-1744j 3.03e-498, 3.03e-498j
10.448964909729461348 - 4.8685971599221841298e-1742j 2.1e-495, 2.1e-495j
-3.6382430676068060947 - 6.7524892108312133623e-1754j 3.23e-500, 3.23e-500j
-4.4677069572407988504 + 8.0608442909505523872e-1750j 1.04e-498, 1.04e-498j
11.574803203521677055 - 9.0984610447206735582e-1759j 4.71e-496, 4.71e-496j
-9.413418928509502288 + 4.1620791555398677699e-1783j 3.68e-495, 3.68e-495j
-6.6107947002797749877 - 1.2673409128261761443e-1816j 3.98e-496, 3.98e-496j
-2.008475226640472094 + 1.9904684500424155619e-1846j 1.06e-503, 1.06e-503j
7.5081723365509911424 - 2.5439284610650603031e-1836j 1.49e-495, 1.49e-495j
-9.9221626372550859863 - 1.4356804765244881533e-1872j 2.71e-495, 2.71e-495j
-3.2555578552247731743e-1921 + 8.8914908530869311472e-1921j 5.78e-1919, 5.78e-1919j
-0.40063821105995049206 - 4.8306169973869973048e-1920j 1.08e-508, 1.08e-508j
-7.5081723365509911424 - 6.7136493797901526344e-1923j 1.49e-495, 1.49e-495j
0.40063821105995049206 - 1.5092097183022316245e-1970j 1.17e-508, 1.17e-508j

Weights

Weight (ball center) Error (ball radius)
0.00089286291334885392657 - 1.6390613397855915873e-1459j 8.84e-137, 7.39e-385j
9.3712287678835697734e-47 + 4.1252527684518348428e-1482j 1.98e-176, 1.65e-424j
1.2734244397327137293e-07 - 5.0988530478672200788e-1462j 3.24e-150, 2.71e-398j
0.04429919014155633415 - 4.7119271004437262723e-1459j 2.4e-121, 2e-369j
1.0935537165661110849e-06 - 3.2873255387107078908e-1461j 3.84e-148, 3.2e-396j
0.0030522259632903189842 + 4.2851403055761002137e-1459j 7.29e-135, 6.09e-383j
0.021440700089215401467 + 4.2268198601740369522e-1459j 1.09e-127, 9.11e-376j
0.0087970077780564754112 - 3.8837125764872514016e-1459j 1.09e-131, 9.09e-380j
0.00021942509449102738995 - 8.7719702567082330097e-1460j 9.73e-142, 8.13e-390j
0.077742307060467862788 + 5.1245742442991446978e-1459j 3.64e-120, 3.04e-368j
4.5111525791571676646e-05 + 1.2054988038197181593e-1460j 1.04e-144, 8.65e-393j
0.1160576513452515956 - 5.327656398774478151e-1459j 4.88e-121, 4.08e-369j
1.2096242825343146554e-08 + 9.5216673199795817704e-1462j 1.64e-154, 1.37e-402j
9.2880342218154709459e-10 + 3.4429751902424102726e-1463j 4.18e-157, 3.49e-405j
7.7204093582151220506e-06 + 2.9377280279648139226e-1461j 3.7e-148, 3.09e-396j
6.5184766419075549797e-17 - 2.95491662789408448e-1467j 8.05e-173, 6.72e-421j
1.3977653698327198173e-33 - 2.0469550440646480119e-1475j 5.6e-178, 4.67e-426j
9.3712287678835697734e-47 - 2.368796589693115651e-1482j 1.76e-186, 1.47e-434j
2.7668880796351236181e-12 - 2.7148009966913704073e-1464j 1.88e-162, 1.57e-410j
5.7039803251286354776e-11 + 1.676583982364146042e-1463j 3.92e-160, 3.27e-408j
4.1939484179227371596e-25 - 2.0352369432694205227e-1471j 2.27e-179, 1.9e-427j
3.7088060732095639449e-37 - 1.6373951689400252098e-1477j 1.76e-184, 1.47e-432j
0.0087970077780564754112 - 6.8063513340030693405e-1460j 3.51e-151, 2.93e-399j
1.9132142559222252681e-30 - 4.0283712592115579912e-1474j 2.6e-182, 2.17e-430j
2.2364824894989936017e-41 + 1.2170528600705840495e-1479j 4.9e-186, 4.09e-434j
2.7668880796351236181e-12 + 6.8662208317811284549e-1465j 1.3e-173, 1.09e-421j
1.2096242825343146554e-08 - 5.1701661829580047547e-1463j 3.86e-170, 3.22e-418j
0.0030522259632903189842 + 3.7584345161003851034e-1460j 1.47e-157, 1.23e-405j
1.0277368048053693301e-18 - 9.394595187352135547e-1468j 1.65e-176, 1.38e-424j
1.3977653698327198173e-33 + 1.0470300880723625938e-1475j 5.13e-184, 4.28e-432j
1.1444908106729465443e-20 + 8.9606813030662158537e-1469j 3.57e-178, 2.99e-426j
0.04429919014155633415 - 1.7618256066419492281e-1459j 9.62e-153, 8.03e-401j
3.7088060732095639449e-37 + 3.0811181512040568016e-1477j 8.17e-187, 6.82e-435j
1.0277368048053693301e-18 + 3.5697033492980753057e-1468j 2.78e-179, 2.32e-427j
0.00089286291334885392657 - 1.9127720930439034298e-1460j 1.04e-163, 8.68e-412j
6.5184766419075549797e-17 + 8.3600414419571856962e-1467j 6.04e-176, 5.05e-424j
4.5111525791571676646e-05 - 3.8426325639917127899e-1461j 5.34e-168, 4.46e-416j
1.2734244397327137293e-07 + 1.7568904755757465185e-1462j 6.97e-172, 5.82e-420j
8.6411169244947932162e-23 - 7.0900289426352216197e-1470j 1.65e-180, 1.38e-428j
1.2179530564067152341e-27 - 2.2418417160169098977e-1472j 1.03e-183, 8.64e-432j
1.0935537165661110849e-06 - 5.4016037329647690864e-1462j 7.16e-172, 5.99e-420j
0.077742307060467862788 + 2.5279058500837388149e-1459j 2.24e-158, 1.87e-406j
9.2880342218154709459e-10 + 1.370069641833210992e-1463j 2.58e-175, 2.15e-423j
3.0158661318419225693e-15 - 6.4417231503195160729e-1466j 1.59e-176, 1.33e-424j
1.2179530564067152341e-27 + 1.0560506819656542773e-1472j 1.48e-185, 1.24e-433j
3.0158661318419225693e-15 + 2.0904244568072801737e-1466j 6.56e-180, 5.48e-428j
0.1160576513452515956 - 3.3690108632726990533e-1459j 4.98e-164, 4.15e-412j
2.2364824894989936017e-41 - 2.2053913427440960397e-1479j 3.81e-191, 3.18e-439j
4.1939484179227371596e-25 + 4.5233945170975528605e-1471j 3.28e-183, 2.75e-431j
0.00021942509449102738995 + 8.9515918769702785623e-1461j 4.54e-172, 3.8e-420j
7.7204093582151220506e-06 + 1.5087902717029952702e-1461j 9.26e-174, 7.75e-422j
1.9132142559222252681e-30 + 8.1960720409900977029e-1474j 2.27e-186, 1.89e-434j
1.1444908106729465443e-20 - 3.6259891422329069387e-1469j 3.15e-184, 2.63e-432j
5.7039803251286354776e-11 - 3.2514293620683634092e-1464j 4.07e-179, 3.58e-427j
0.021440700089215401467 + 1.1383753332098428436e-1459j 6.83e-173, 5.75e-421j
1.0446062071534588904e-13 + 4.3853799911904706513e-1465j 1.17e-179, 9.77e-428j
8.6411169244947932162e-23 + 3.0336873683294486363e-1470j 2.28e-185, 1.8e-433j
0.15981414117778535617 - 4.8360416564857049496e-1459j 1.29e-173, 8.63e-422j
0.14753749310915864445 + 4.178988159612688425e-1459j 1.2e-173, 8.44e-422j
1.0446062071534588904e-13 - 1.2805617301595080132e-1465j 4.15e-181, 4.06e-429j
0.14753749310915864445 + 5.2366063349748591475e-1459j 1.06e-173, 6.63e-422j

Download

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