Rule: Q[43]

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)
8.1804905114486618262 - 1.6128772932259508819e-565j 7.03e-245, 7.03e-245j
10.176437001879133613 + 1.4772228609560335833e-582j 1e-245, 1e-245j
-11.932057301056317452 + 4.9600481283223902847e-597j 1.09e-247, 1.09e-247j
-9.4630967355223121218 + 7.5803942145463174741e-594j 2.42e-245, 2.42e-245j
8.8029547057222341609 - 4.642068743843465014e-601j 5.18e-245, 5.18e-245j
11.932057301056317452 + 1.6404535599389251656e-611j 1.11e-247, 1.11e-247j
-10.176437001879133613 + 1.9006995368700329997e-618j 7.72e-246, 7.72e-246j
-10.973099524957786382 - 2.364933483028415831e-620j 1.41e-246, 1.41e-246j
7.5863830525708615775 - 4.6760380803429922987e-617j 8.25e-245, 8.25e-245j
-8.1804905114486618262 + 2.1688474003521655479e-626j 7.25e-245, 7.25e-245j
10.973099524957786382 - 4.1959426225632686673e-626j 1.37e-246, 1.37e-246j
-5.3936834231253809986 - 1.5495489475604940798e-635j 1.01e-245, 1.01e-245j
-8.8029547057222341609 + 1.9513352115735119133e-632j 5.08e-245, 5.08e-245j
-5.9209784614715200246 - 5.3770753715444585551e-633j 2.27e-245, 2.27e-245j
-7.5863830525708615775 - 5.3972508370793992491e-633j 7.97e-245, 7.97e-245j
9.4630967355223121218 - 8.2811705978570149912e-632j 2.49e-245, 2.49e-245j
5.9209784614715200246 - 1.2944742948773453948e-655j 2.18e-245, 2.18e-245j
-3.3712358171480526595 - 6.8356137262925232333e-674j 4.89e-248, 4.89e-248j
-7.0144733541827294045 - 5.2434320734360528165e-670j 6.84e-245, 6.84e-245j
-6.4604133308954666008 + 5.0031231555571812239e-675j 5.16e-245, 5.16e-245j
2.3947734288425255683 + 3.8848877753888327428e-683j 1.31e-249, 1.31e-249j
0.95345327562973769009 - 1.0805403749724763341e-695j 1.11e-252, 1.11e-252j
4.8765512847065944515 - 6.8374466695729849578e-705j 3.42e-246, 3.42e-246j
-1.9119592749517121403 - 9.8909601427108011709e-730j 1.47e-250, 1.47e-250j
-1.4317493644516902135 + 5.6414207464112073358e-735j 1.4e-251, 1.4e-251j
1.9119592749517121403 + 1.1305222039082311332e-733j 1.69e-250, 1.69e-250j
6.4604133308954666008 - 1.6536526560313805593e-738j 5.04e-245, 5.04e-245j
2.8809307774503764409 - 3.4656122909499867875e-761j 1.05e-248, 1.05e-248j
7.0144733541827294045 + 1.1880494032610171223e-764j 6.65e-245, 6.65e-245j
-2.3947734288425255683 - 2.5652992516728169635e-778j 1.32e-249, 1.32e-249j
-4.8765512847065944515 + 1.9042750346815668898e-773j 3.97e-246, 3.97e-246j
3.8665796556922060917 - 2.454030848563472436e-772j 2.92e-247, 2.92e-247j
1.3726585854899860454e-799 + 1.5968621561675124576e-798j 6.89e-797, 6.89e-797j
4.3679669348066756788 - 4.415365088251908798e-775j 1.25e-246, 1.25e-246j
-4.3679669348066756788 - 3.9921867239679269985e-783j 1.02e-246, 1.02e-246j
3.3712358171480526595 - 3.1377656200317623145e-781j 4.9e-248, 4.9e-248j
5.3936834231253809986 - 3.5303502794361456175e-792j 1.16e-245, 1.16e-245j
0.47641488610849427988 + 1.5486817292664995534e-816j 6.1e-254, 6.1e-254j
-3.8665796556922060917 - 9.0949293898810518941e-809j 2.64e-247, 2.64e-247j
-0.47641488610849427988 - 1.4527919974460463716e-817j 6.1e-254, 6.1e-254j
-0.95345327562973769009 - 2.0769745441068044466e-816j 9.32e-253, 9.32e-253j
-2.8809307774503764409 - 3.9624819336851374079e-811j 1.07e-248, 1.07e-248j
1.4317493644516902135 - 9.1048482438429187002e-811j 1.4e-251, 1.4e-251j

Weights

Weight (ball center) Error (ball radius)
7.121219095949836797e-16 + 4.6979135974016017922e-580j 5.08e-79, 2.75e-201j
9.7059611743871922575e-24 + 6.7181374097248718448e-585j 4.03e-83, 2.18e-205j
5.3520752240799096366e-32 - 4.9507673319260165452e-590j 2.67e-87, 1.44e-209j
9.772188868028616492e-21 + 2.4115015105670532348e-584j 1.73e-83, 9.33e-206j
3.79745385179088823e-18 + 1.3474429278280357307e-581j 2.98e-81, 1.61e-203j
5.3520752240799096366e-32 + 2.654158922287590672e-589j 2.34e-87, 1.27e-209j
9.7059611743871922575e-24 - 7.3046226147782992772e-586j 4.89e-85, 2.64e-207j
2.4385097855866963231e-27 + 1.1096616204427818652e-587j 1.88e-86, 1.01e-208j
7.3864287975093105214e-14 - 1.9689321689041214279e-579j 5.03e-81, 2.72e-203j
7.121219095949836797e-16 + 7.0201490753337243195e-582j 5.13e-83, 2.77e-205j
2.4385097855866963231e-27 - 7.610805398922721554e-587j 3.74e-87, 2.02e-209j
1.0030066755417815115e-07 - 1.0041925697604939356e-577j 6.18e-79, 3.34e-201j
3.79745385179088823e-18 - 4.9385443629076462267e-583j 6.93e-84, 3.74e-206j
5.1867054608185025639e-09 + 2.1981632286014714021e-578j 2.07e-80, 1.12e-202j
7.3864287975093105214e-14 - 7.419082057205078743e-581j 5.85e-83, 3.16e-205j
9.772188868028616492e-21 - 3.3172720121970123219e-583j 3.1e-87, 1.68e-209j
5.1867054608185025639e-09 + 1.3718594935508878654e-577j 1.74e-83, 9.41e-206j
0.00066916839169690166212 - 9.638275134954545723e-576j 2.45e-77, 1.32e-199j
4.6416475761066535806e-12 + 6.1026000951803530492e-580j 7.89e-83, 4.26e-205j
1.884798249393542386e-10 - 4.0359246385520199326e-579j 3.83e-82, 2.07e-204j
0.01098373316809109537 - 7.7964391824421862855e-575j 1.36e-77, 7.36e-200j
0.12093036830966250338 + 2.0710276498315844523e-574j 1.45e-73, 7.85e-196j
1.4020888279499707889e-06 + 1.5425321191009431049e-576j 6.61e-84, 3.57e-206j
0.030875167245633445184 + 7.4935319565913530325e-575j 1.28e-75, 6.91e-198j
0.068587049431093171781 - 1.1726676958417873774e-574j 1.44e-73, 7.78e-196j
0.030875167245633445184 + 1.2064723320569765579e-574j 1.57e-76, 8.49e-199j
1.884798249393542386e-10 - 3.4352868124780170457e-578j 4.85e-86, 2.62e-208j
0.0030700123957878347397 + 4.4999612551286184129e-575j 6.63e-81, 3.58e-203j
4.6416475761066535806e-12 + 7.9526092180404843856e-579j 1.05e-86, 5.66e-209j
0.01098373316809109537 - 4.2654246377243174749e-575j 3.08e-80, 1.66e-202j
1.4020888279499707889e-06 + 3.9032059913508549932e-577j 2.53e-84, 1.37e-206j
0.00011268240163838016711 + 1.0590961335320306196e-575j 4.86e-84, 2.63e-206j
0.19002072478258652824 + 2.293504737416842711e-574j 2.61e-79, 1.41e-201j
1.4488711829612319205e-05 - 4.2971533359812523602e-576j 1.07e-84, 5.77e-207j
1.4488711829612319205e-05 - 1.3055786718042573527e-576j 3.1e-85, 1.68e-207j
0.00066916839169690166212 - 2.3150929554772732871e-575j 8.04e-84, 4.34e-206j
1.0030066755417815115e-07 - 4.8912910631130712556e-577j 4.98e-86, 2.69e-208j
0.16974545978387677358 - 2.3017441488701564245e-574j 3.55e-82, 1.92e-204j
0.00011268240163838016711 + 3.7924958054908053768e-576j 3.95e-85, 2.14e-207j
0.16974545978387677358 - 2.0484006903995791819e-574j 6.02e-83, 3.23e-205j
0.12093036830966250338 + 1.6386562355373237627e-574j 4.02e-83, 2.15e-205j
0.0030700123957878347397 + 2.1559447786483886947e-575j 1.63e-84, 8.87e-207j
0.068587049431093171781 - 1.670231964988962138e-574j 1.13e-83, 5.53e-206j

Download

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