Rule: Q[17]

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.

$P_{1}$ :
$131072 \cdot t^{17} - 8912896 \cdot t^{15} + 233963520 \cdot t^{13} - 3041525760 \cdot t^{11} + 20910489600 \cdot t^{9} - 75277762560 \cdot t^{7} + 131736084480 \cdot t^{5} - 94097203200 \cdot t^{3} + 17643225600 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-2.7577629157038887309 + 1.1455482795355022454e-186j	4.13e-60, 4.13e-60j
3.3789320911414940834 + 7.9781860303905870647e-191j	4.93e-60, 4.93e-60j
-4.8713451936744030883 + 2.3515563179344686696e-199j	1.35e-60, 1.35e-60j
4.8713451936744030883 + 6.0199841739122397942e-197j	1.63e-60, 1.63e-60j
-4.0619466758754743069 + 2.939445397418085837e-200j	3.04e-60, 3.04e-60j
1.6129243142212313331 - 2.5475193444290077254e-199j	5.06e-61, 5.06e-61j
-1.6271087185081542211e-285 - 2.62806898124642894e-207j	4.47e-206, 4.47e-206j
-0.53163300134265473135 + 8.978992346204813098e-205j	9.2e-63, 9.2e-63j
-2.1735028266666208193 + 7.4953306032253707867e-203j	1.68e-60, 1.68e-60j
-3.3789320911414940834 + 3.9868779804390270142e-204j	5.97e-60, 5.97e-60j
1.0676487257434505536 - 2.0931109397304891825e-204j	7.58e-62, 7.58e-62j
2.7577629157038887309 + 1.1938855036333603692e-208j	3.95e-60, 3.95e-60j
-1.6129243142212313331 - 4.815840218516844064e-218j	4.61e-61, 4.61e-61j
-1.0676487257434505536 - 1.8147927294043254285e-219j	7.58e-62, 7.58e-62j
4.0619466758754743069 + 1.9787209020202393523e-226j	3.92e-60, 3.92e-60j
2.1735028266666208193 - 3.0663966836855247184e-243j	1.66e-60, 1.66e-60j
0.53163300134265473135 - 1.0649848921181807323e-249j	9.2e-63, 9.2e-63j

Weights

Weight (ball center)	Error (ball radius)
0.00016849143155133847317 + 5.3229013896822977142e-190j	1.73e-21, 1.58e-50j
4.0126794479798523561e-06 - 4.854916648903468838e-192j	1.36e-23, 1.24e-52j
2.584314919374907689e-11 + 3.5764706904720645281e-194j	6.32e-26, 5.76e-55j
2.584314919374907689e-11 - 9.9078037143844615315e-195j	1.28e-26, 1.17e-55j
2.8080161179305686591e-08 - 1.9105680000388432042e-192j	9.56e-25, 8.72e-54j
0.023086657025710961025 + 5.1694537708458840331e-190j	2.92e-21, 2.66e-50j
0.29953837012660542072 - 2.9510422072154814322e-189j	1.87e-20, 1.69e-49j
0.22670630846897692753 + 3.1804330774002082152e-189j	1.26e-20, 1.14e-49j
0.0028589460622846210812 - 1.360816476748929406e-189j	3.47e-22, 3.17e-51j
4.0126794479798523561e-06 + 4.795227495894326047e-191j	7.95e-24, 7.25e-53j
0.097406371162721133173 - 1.2131808318705494456e-189j	1.47e-21, 1.33e-50j
0.00016849143155133847317 + 3.4998202407297260632e-191j	2.04e-24, 1.87e-53j
0.023086657025710961025 + 1.9735113984201365507e-189j	3.61e-22, 3.27e-51j
0.097406371162721133173 - 2.7458810233549069485e-189j	8.45e-22, 7.71e-51j
2.8080161179305686591e-08 + 3.6533359983362262881e-193j	1.84e-26, 1.66e-55j
0.0028589460622846210812 - 1.6123747041099742843e-190j	6.7e-24, 6.28e-53j
0.22670630846897692753 + 2.1524018345073795523e-189j	2.45e-22, 1.86e-51j

Download

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