Rule: Q[14]

Type

This rule is of Hermite (probabilists') 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.

$P_{1}$ :
$t^{14} - 91 \cdot t^{12} + 3003 \cdot t^{10} - 45045 \cdot t^{8} + 315315 \cdot t^{6} - 945945 \cdot t^{4} + 945945 \cdot t^{2} - 135135$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.41259045795460183817 + 4.7733380679681323157e-153j	4.11e-63, 4.11e-63j
-4.8969363973455646837 - 1.7900017754880496184e-153j	1.4e-60, 1.4e-60j
-3.8869245750597693838 - 7.4024031757162051927e-153j	1.22e-60, 1.22e-60j
-6.0874095469012913223 + 1.7631983634852988754e-153j	4.39e-61, 4.39e-61j
-2.088344745701944171 + 1.3126679686912363868e-152j	1.68e-61, 1.68e-61j
-1.242688955485464179 - 1.8645851828000516858e-153j	4.62e-62, 4.62e-62j
2.088344745701944171 - 6.0860060366593687025e-152j	1.93e-61, 1.93e-61j
1.242688955485464179 + 1.2746187773047228321e-156j	3.02e-62, 3.02e-62j
-2.9630365798386675025 - 4.836723038879528604e-159j	7.91e-61, 7.91e-61j
-0.41259045795460183817 - 3.1257544914633902111e-163j	4.11e-63, 4.11e-63j
3.8869245750597693838 - 5.5277777897783914739e-176j	1.17e-60, 1.17e-60j
6.0874095469012913223 + 2.468854050723065184e-189j	4.43e-61, 4.43e-61j
4.8969363973455646837 + 2.939445397418085837e-199j	1.25e-60, 1.25e-60j
2.9630365798386675025 - 1.9771352289469662165e-208j	7.21e-61, 7.21e-61j

Weights

Weight (ball center)	Error (ball radius)
0.30263462681301950107 + 2.8323756815856556392e-153j	3.93e-17, 2.03e-47j
2.6609913440676305554e-06 + 3.632034064240976891e-156j	3.41e-21, 1.77e-51j
0.00020033955376074414217 - 4.6766002490265006135e-155j	3.51e-20, 1.81e-50j
4.8681612577483808128e-09 - 1.2631498617583508711e-157j	8.71e-23, 4.51e-53j
0.03865010882425340019 - 8.430590932369629454e-156j	2.04e-18, 1.06e-48j
0.15408333984251362572 - 5.7384126590394440577e-154j	2.9e-17, 1.5e-47j
0.03865010882425340019 + 2.60279756871407714e-153j	8e-20, 4.14e-50j
0.15408333984251362572 - 6.3838000947634046073e-153j	3.64e-18, 1.88e-48j
0.0044289191069474034969 + 3.3797534556982955113e-154j	1.11e-19, 5.73e-50j
0.30263462681301950107 + 4.3460244963357998756e-154j	4.39e-18, 2.27e-48j
0.00020033955376074414217 - 9.1410513724813550043e-155j	3.93e-23, 2.03e-53j
4.8681612577483808128e-09 - 2.047504740411998343e-157j	7.58e-26, 3.92e-56j
2.6609913440676305554e-06 + 6.7724640383515229825e-156j	1.41e-24, 7.32e-55j
0.0044289191069474034969 + 8.8642398966927941591e-154j	8.75e-23, 4.48e-53j

Download

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