Rule: Q[20]

Type

This rule is of Hermite (physicists') type.

Polynomials

One starts from the polynomial $P_{1}$ and extends one by one with $P_{i}$ 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.

$P_{1}$ :
$1048576 \cdot t^{20} - 99614720 \cdot t^{18} + 3810263040 \cdot t^{16} - 76205260800 \cdot t^{14} + 866834841600 \cdot t^{12} - 5721109954560 \cdot t^{10} + 21454162329600 \cdot t^{8} - 42908324659200 \cdot t^{6} + 40226554368000 \cdot t^{4} - 13408851456000 \cdot t^{2} + 670442572800$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
2.7888060584281304805 - 1.6388149971404892316e-328j	2.81e-123, 2.81e-123j
-3.3478545673832163269 + 2.8718868024196464779e-343j	4.56e-123, 4.56e-123j
4.6036824495507442731 + 1.1132225727917710102e-357j	3.62e-123, 3.62e-123j
0.2453407083009012499 + 8.4513358251097134537e-372j	5.39e-127, 5.39e-127j
3.3478545673832163269 - 5.3748937400532151789e-377j	4.9e-123, 4.9e-123j
-1.2340762153953230079 - 4.7422292033476776964e-380j	4.63e-125, 4.63e-125j
-5.387480890011232862 + 5.1018779721894791736e-383j	8e-124, 8e-124j
-4.6036824495507442731 + 6.6487750598024851001e-383j	3.18e-123, 3.18e-123j
-1.7385377121165862068 + 4.4004898517189858032e-383j	2.47e-124, 2.47e-124j
5.387480890011232862 + 4.6233967612383754771e-382j	8.43e-124, 8.43e-124j
0.73747372854539435871 + 1.1634755851126548845e-385j	5.3e-126, 5.3e-126j
2.2549740020892755231 - 1.2095102793824852315e-389j	1.17e-123, 1.17e-123j
-0.2453407083009012499 + 3.6911324444045569809e-394j	5.39e-127, 5.39e-127j
-3.9447640401156252104 - 3.0420821075007963991e-396j	6.33e-123, 6.33e-123j
-2.7888060584281304805 - 1.264348308593239437e-396j	3.04e-123, 3.04e-123j
-2.2549740020892755231 + 1.6009161898764289847e-397j	9.21e-124, 9.21e-124j
1.7385377121165862068 + 4.7959216349176603913e-398j	2.68e-124, 2.68e-124j
3.9447640401156252104 - 1.8152313867298734275e-406j	6.14e-123, 6.14e-123j
-0.73747372854539435871 + 5.1220299924674563448e-416j	3.85e-126, 3.85e-126j
1.2340762153953230079 - 6.2193929698859454662e-436j	3.48e-125, 3.48e-125j

Weights

Weight (ball center)	Error (ball radius)
0.0001288262799619294494 + 5.8877953870310199e-332j	5.14e-47, 6.5e-108j
4.4021210902308528331e-06 + 6.3596182758636483413e-334j	2.42e-49, 3.06e-110j
2.4820623623151786456e-10 + 1.6146985528647442457e-335j	1.1e-51, 1.38e-112j
0.26079306344955485915 - 3.7346882478999296199e-331j	2.06e-43, 2.6e-104j
4.4021210902308528331e-06 + 6.9809360804176408589e-333j	8.06e-49, 1.02e-109j
0.061506372063976906552 + 1.1467134189517820015e-331j	2.05e-43, 2.58e-104j
1.2578006724379270154e-13 - 8.0682983509110080051e-338j	3.85e-54, 4.86e-115j
2.4820623623151786456e-10 + 3.964129642151136654e-336j	7.08e-53, 8.95e-114j
0.01399783744710100335 - 4.8609277160505586314e-332j	1.68e-47, 2.12e-108j
1.2578006724379270154e-13 - 2.5385524075930927027e-337j	7.87e-55, 9.95e-116j
0.16173933398399996172 + 3.6467329669474119899e-331j	8.35e-46, 1.05e-106j
0.0018301031310804927956 - 1.4906143413553359589e-331j	2.45e-49, 3.1e-110j
0.26079306344955485915 + 3.1307154473286453735e-331j	5.65e-46, 7.14e-107j
6.1274902599829475405e-08 - 6.8379841823535486693e-335j	5.15e-52, 6.5e-113j
0.0001288262799619294494 - 3.7851760790140067365e-333j	1.27e-50, 1.6e-111j
0.0018301031310804927956 + 1.5776614156571270021e-332j	5.47e-50, 6.89e-111j
0.01399783744710100335 + 2.095377899526032714e-331j	7.02e-50, 8.64e-111j
6.1274902599829475405e-08 - 3.9831937279757356796e-334j	7.29e-53, 9.48e-114j
0.16173933398399996172 - 2.1214032026564726249e-331j	3.58e-49, 5.32e-110j
0.061506372063976906552 - 2.9671348414190469029e-331j	1.6e-49, 1.81e-110j

Download

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