Rule: Q[18]

Type

This rule is of Chebyshev U (second kind) 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.

$P_{1}$ :
$262144 \cdot t^{18} - 1114112 \cdot t^{16} + 1966080 \cdot t^{14} - 1863680 \cdot t^{12} + 1025024 \cdot t^{10} - 329472 \cdot t^{8} + 59136 \cdot t^{6} - 5280 \cdot t^{4} + 180 \cdot t^{2} - 1$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.9863613034027223736 - 2.576291728571601929e-461j	5.73e-123, 5.73e-123j
-0.40169542465296945752 + 1.3437834740894176163e-472j	2.47e-125, 2.47e-125j
-0.94581724170063467902 - 1.1237805760229264132e-477j	1.48e-122, 1.48e-122j
-0.54694815812242687471 + 2.5242790429503886726e-486j	3.04e-124, 3.04e-124j
0.87947375120648907139 + 1.8211488153919763605e-487j	9.93e-123, 9.93e-123j
0.94581724170063467902 - 1.0092802095626857075e-491j	1.29e-122, 1.29e-122j
-0.9863613034027223736 - 3.7155114525802263735e-490j	7.41e-123, 7.41e-123j
-0.87947375120648907139 + 2.5245429068569211469e-491j	1.22e-122, 1.22e-122j
-0.78914050939639359922 + 4.5161681250932395834e-501j	6.33e-123, 6.33e-123j
0.40169542465296945752 + 2.442710563969575358e-503j	2.91e-125, 2.91e-125j
0.78914050939639359922 + 3.2784970992805667743e-503j	4.99e-123, 4.99e-123j
0.24548548714079914892 + 5.7286002259679105138e-507j	2.19e-126, 2.19e-126j
-0.67728157162574107476 + 5.3057852447704058242e-505j	1.63e-123, 1.63e-123j
0.0825793454723323246 + 1.0492845569217153671e-510j	1.36e-127, 1.36e-127j
-0.24548548714079914892 + 1.0410200170254792826e-515j	2.19e-126, 2.19e-126j
0.67728157162574107476 - 3.0703114192900953181e-518j	1.57e-123, 1.57e-123j
0.54694815812242687471 + 2.4427727333573941907e-525j	3.18e-124, 3.18e-124j
-0.0825793454723323246 - 2.5286748875094607541e-533j	1.36e-127, 1.36e-127j

Weights

Weight (ball center)	Error (ball radius)
0.00142586206050961371 + 2.0061745794784445353e-462j	1.62e-44, 5.5e-105j
0.044138988726993186178 - 8.1923821459056178051e-463j	7.92e-45, 2.69e-105j
0.0055489339632528000206 + 7.3987327456936861498e-464j	1.28e-45, 4.35e-106j
0.036886721701393933093 + 6.1977675350761237389e-463j	5.02e-45, 1.71e-105j
0.011922416891515082244 + 2.8736390151202005698e-462j	7e-46, 2.38e-106j
0.0055489339632528000206 - 3.5259596773896656193e-462j	8.83e-46, 3e-106j
0.00142586206050961371 - 1.8621151397399281362e-464j	1.1e-46, 3.75e-107j
0.011922416891515082244 - 1.6462132570047299538e-463j	1.6e-46, 5.43e-107j
0.01985564507524212766 + 2.8810972653064875967e-463j	9.44e-47, 3.2e-107j
0.044138988726993186178 + 1.9449554984738218015e-462j	2.43e-48, 8.23e-109j
0.01985564507524212766 - 2.5937393889162644651e-462j	1.58e-48, 5.36e-109j
0.049459835558065501879 - 1.7198964043246191515e-462j	1.88e-48, 6.37e-109j
0.028488930144008745384 - 4.4117518362779147585e-463j	1.15e-47, 3.9e-108j
0.052272665879019009832 + 1.4900677707881961392e-462j	6.25e-49, 2.12e-109j
0.049459835558065501879 + 1.0344059522474573548e-462j	9.02e-49, 3.09e-109j
0.028488930144008745384 + 2.3746557130673811271e-462j	7.09e-50, 2.46e-110j
0.036886721701393933093 - 2.162678951094539508e-462j	7.56e-50, 2.63e-110j
0.052272665879019009832 - 1.2598420396293852457e-462j	8.16e-50, 2.55e-110j

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.