Rule: Q[17]

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.

$P_{1}$ :
$t^{17} - 136 \cdot t^{15} + 7140 \cdot t^{13} - 185640 \cdot t^{11} + 2552550 \cdot t^{9} - 18378360 \cdot t^{7} + 64324260 \cdot t^{5} - 91891800 \cdot t^{3} + 34459425 \cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Node (ball center)	Error (ball radius)
-5.7444600786594061813 + 1.5996863105054560013e-333j	1e-123, 1e-123j
-4.7785315896299838271 - 1.9828484069386292156e-352j	1.16e-123, 1.16e-123j
-6.8891224398953322326 - 4.3954864854185204756e-364j	3.23e-124, 3.23e-124j
3.0737971753281935585 + 1.2305144961359742789e-369j	3.38e-124, 3.38e-124j
5.7444600786594061813 + 8.319283702842374181e-373j	8.9e-124, 8.9e-124j
6.8891224398953322326 - 6.2463619846916465059e-378j	4.64e-124, 4.64e-124j
-3.0737971753281935585 + 6.6430563446065393788e-379j	3.79e-124, 3.79e-124j
-1.5098833077967407591 - 2.4020141112003197616e-385j	1.8e-125, 1.8e-125j
-2.2810194402529888954 + 1.6213595250602158391e-385j	1.3e-124, 1.3e-124j
-3.0924978734211270124e-391 + 2.1991095988772458755e-390j	3.78e-389, 3.78e-389j
0.75184260070389617074 + 1.2828139326783934274e-390j	2.3e-126, 2.3e-126j
3.900065717198009909 + 5.5124347278522963279e-388j	8.04e-124, 8.04e-124j
4.7785315896299838271 + 9.7870936025878404798e-396j	1.4e-123, 1.4e-123j
-0.75184260070389617074 + 2.0000785287968445805e-402j	1.51e-126, 1.51e-126j
-3.900065717198009909 - 2.6073205159344166217e-413j	8.72e-124, 8.72e-124j
2.2810194402529888954 + 7.2794752034590621291e-425j	1.1e-124, 1.1e-124j
1.5098833077967407591 - 1.5673873412010951276e-439j	2e-125, 2e-125j

Weights

Weight (ball center)	Error (ball radius)
2.8080161179305686591e-08 + 1.2901899201828365552e-340j	5.29e-50, 8.05e-112j
4.0126794479798523561e-06 - 5.5591307018036896952e-340j	4.86e-49, 7.41e-111j
2.584314919374907689e-11 + 1.1905014844103637389e-342j	1.47e-51, 2.24e-113j
0.0028589460622846210812 - 1.6253797438934935207e-339j	1.65e-48, 2.51e-110j
2.8080161179305686591e-08 + 3.9098060409713015034e-342j	1.17e-52, 1.78e-114j
2.584314919374907689e-11 - 1.0786506821787357947e-343j	6.06e-54, 9.23e-116j
0.0028589460622846210812 - 5.3668385849802406292e-339j	2.01e-49, 3.06e-111j
0.097406371162721133173 - 1.9756877074143614934e-338j	3.37e-47, 5.13e-109j
0.023086657025710961025 + 1.1760002215642091717e-338j	1.4e-48, 2.13e-110j
0.29953837012660542072 - 2.5539455975897024734e-338j	2.43e-47, 3.7e-109j
0.22670630846897692753 + 1.9647177894813583552e-338j	1.56e-47, 2.38e-109j
0.00016849143155133847317 + 3.6078016888524956875e-340j	1.15e-51, 1.76e-113j
4.0126794479798523561e-06 - 5.1028480192488915515e-341j	1.58e-52, 2.41e-114j
0.22670630846897692753 + 2.5564549049383890232e-338j	8.27e-49, 1.26e-110j
0.00016849143155133847317 + 1.886556214957509612e-339j	2.48e-51, 3.78e-113j
0.023086657025710961025 + 5.0750948258508578193e-339j	6.67e-51, 1.02e-112j
0.097406371162721133173 - 1.1532678874721398244e-338j	1.78e-50, 2.65e-112j

Download

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