Rule: Q[1, 8]

Type

This rule is of Legendre 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.

$P_{1}$ :
$t$
$P_{2}$ :
$t^{9} - \frac{36}{17} \cdot t^{7} + \frac{126}{85} \cdot t^{5} - \frac{84}{221} \cdot t^{3} + \frac{63}{2431} \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
0.96816023950762608984 + 7.1092636020535081473e-180j	8.64e-62, 8.64e-62j
-0.61337143270059039731 + 5.5158688318700045419e-186j	4.11e-62, 4.11e-62j
-0.96816023950762608984 - 3.3755968111704454879e-187j	8.52e-62, 8.52e-62j
0.32425342340380892904 + 1.1506999082294115959e-192j	4.57e-63, 4.57e-63j
0.8360311073266357943 + 3.0368797116625401085e-206j	9.13e-62, 9.13e-62j
0.61337143270059039731 - 1.3456024139973534885e-218j	4.18e-62, 4.18e-62j
-2.0051038473805092103e-226 - 6.3319068864647659273e-226j	5.98e-225, 5.98e-225j
-0.8360311073266357943 + 3.6585725011311717191e-229j	1.23e-61, 1.23e-61j
-0.32425342340380892904 - 3.3809740856039640168e-234j	4.57e-63, 4.57e-63j

Weights

Weight (ball center)	Error (ball radius)
0.081274388361574411972 - 8.9267899770954842168e-180j	1.19e-23, 4.04e-54j
0.26061069640293546232 - 2.0640419518372130206e-180j	4.59e-24, 1.56e-54j
0.081274388361574411972 - 2.9840270069145762974e-181j	2.51e-24, 8.52e-55j
0.31234707704000284007 + 6.6475162604811679615e-180j	2.38e-24, 8.07e-55j
0.18064816069485740406 + 1.4289771108132411077e-179j	1.07e-24, 3.62e-55j
0.26061069640293546232 - 9.2008226319347626766e-180j	1.01e-24, 3.43e-55j
0.33023935500125976316 - 4.8056621862494894819e-180j	2.14e-25, 7.35e-56j
0.18064816069485740406 + 1.0465093347196222683e-180j	3.18e-26, 1.25e-56j
0.31234707704000284007 + 3.3119227444752057185e-180j	9.1e-26, 2.87e-56j

Download

All rules of Legendre type can be downloaded here packed into a single file.