Rule: Q[44]

Type

This rule is of Chebyshev T (first kind) type.

Polynomials

One starts from the polynomial P1 and extends one by one with Pi 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.

Node locations in the complex plane

Plot of the node locations in the complex plane.

Magnitude of the Weights

Logarithmic magnitude of the weights
         plotted against the (real part) of the nodes.

Quadrature Rule Data

Nodes

Node (ball center) Error (ball radius)
-0.99936282565699169131 - 2.5347185960572299502e-876j 1.04e-240, 1.04e-240j
0.98411120433611610614 - 1.7692403597654519424e-879j 3.48e-240, 3.48e-240j
-0.92387953251128675613 - 4.4672499816084977141e-894j 9.63e-241, 9.63e-241j
0.99936282565699169131 + 1.2971882783946540282e-903j 1.08e-240, 1.08e-240j
0.96893730178150732995 - 5.2749549050308050593e-923j 2.95e-240, 2.95e-240j
0.92387953251128675613 - 7.2835653380597642237e-941j 1.12e-240, 1.12e-240j
-0.8600142402077005234 + 3.1075036979601008502e-950j 1.45e-241, 1.45e-241j
-0.8942252698597112824 + 2.7445105340568481708e-949j 4.5e-241, 4.5e-241j
0.8942252698597112824 + 9.9396409216406185607e-953j 4.85e-241, 4.85e-241j
-0.98411120433611610614 - 1.0472204737739325221e-952j 3.18e-240, 3.18e-240j
0.8600142402077005234 - 3.1422688372389791355e-962j 1.7e-241, 1.7e-241j
-0.99427030177189731837 + 9.1972712797845938672e-960j 2.89e-240, 2.89e-240j
-0.96893730178150732995 + 6.6097280650708880554e-966j 2.91e-240, 2.91e-240j
-0.82142077512049156131 - 6.7644778031900703968e-974j 4.58e-242, 4.58e-242j
0.99427030177189731837 - 1.6070465674942978476e-971j 2.7e-240, 2.7e-240j
0.82142077512049156131 + 5.073367117512780915e-980j 4.62e-242, 4.62e-242j
0.31579958761502491553 - 1.8513570681134709537e-995j 3.65e-250, 3.65e-250j
-0.51027003306089961332 + 9.5392135523808088522e-992j 1.03e-246, 1.03e-246j
-0.77864153804975517562 + 2.1684271938057051226e-988j 1.18e-242, 1.18e-242j
-0.94882591683731963814 + 3.3510485875129952938e-986j 2.23e-240, 2.23e-240j
0.24730650055421550199 + 7.3615729406425522121e-998j 2.21e-251, 2.21e-251j
0.68141793959389110718 + 1.4478684184479291093e-986j 4.66e-244, 4.66e-244j
0.94882591683731963814 - 7.0045592492260524325e-990j 1.88e-240, 1.88e-240j
-0.68141793959389110718 + 2.5125755152477313405e-1001j 4.67e-244, 4.67e-244j
-0.731894522181725425 - 1.8680048814032369228e-1001j 2.67e-243, 2.67e-243j
0.10689512156511278441 + 3.6384664349198245118e-1013j 6e-254, 6e-254j
0.731894522181725425 - 2.0122425639783024682e-1001j 2.95e-243, 2.95e-243j
0.77864153804975517562 - 3.3982168406374033939e-1007j 1.24e-242, 1.24e-242j
-0.10689512156511278441 + 6.681765152910051743e-1018j 4.54e-254, 4.54e-254j
-0.62746900738085196925 - 4.9749247399521152883e-1008j 7.14e-245, 7.14e-245j
-0.31579958761502491553 + 5.7992123163383751167e-1015j 3.55e-250, 3.55e-250j
0.51027003306089961332 + 1.5893154732118014399e-1011j 1.09e-246, 1.09e-246j
0.62746900738085196925 + 1.6863264469728608161e-1009j 7.45e-245, 7.45e-245j
0.03569233383898045576 - 1.3477265648202834545e-1022j 2.32e-255, 2.32e-255j
-0.38268343236508977173 + 8.8101424317253596237e-1014j 5.44e-249, 5.44e-249j
-0.44761721006271254934 + 1.1793892712006398214e-1011j 8.23e-248, 8.23e-248j
-0.03569233383898045576 - 1.6800331999573755759e-1022j 2.32e-255, 2.32e-255j
0.57032263693496406021 - 9.1322035377750316706e-1012j 8.56e-246, 8.56e-246j
0.17755319625430326814 - 9.2746165307954748237e-1020j 1.08e-252, 1.08e-252j
-0.24730650055421550199 + 8.5458162441632149719e-1017j 2.08e-251, 2.08e-251j
-0.57032263693496406021 + 1.7215551572756924236e-1013j 9.99e-246, 9.99e-246j
-0.17755319625430326814 + 2.0448412471197329421e-1021j 1.08e-252, 1.08e-252j
0.38268343236508977173 + 6.5283129722770753026e-1017j 5.41e-249, 5.41e-249j
0.44761721006271254934 + 9.6463091915860437414e-1017j 9.52e-248, 9.52e-248j

Weights

Weight (ball center) Error (ball radius)
0.022727272727272727273 - 2.259542190500796802e-875j 1.02e-70, 1.06e-186j
0.022727272727272727273 + 1.4510640501598756116e-877j 4.24e-71, 4.42e-187j
0.022727272727272727273 + 8.1826384159522367277e-876j 1.7e-71, 1.77e-187j
0.022727272727272727273 + 2.8291998792834353646e-878j 1.57e-71, 1.64e-187j
0.022727272727272727273 - 2.0648090754266416558e-877j 2.17e-71, 2.26e-187j
0.022727272727272727273 - 3.2258875300442571151e-877j 4.32e-72, 4.51e-188j
0.022727272727272727273 + 5.9102279633112801598e-876j 2.55e-73, 2.66e-189j
0.022727272727272727273 - 6.8715456915463164073e-876j 4.23e-73, 4.42e-189j
0.022727272727272727273 + 3.8265311175301918191e-877j 1.71e-73, 1.79e-189j
0.022727272727272727273 - 1.878949385517515646e-875j 3.78e-74, 3.94e-190j
0.022727272727272727273 - 4.4386082186683771061e-877j 1.17e-74, 1.22e-190j
0.022727272727272727273 + 3.3878727988515248232e-875j 4.06e-74, 4.23e-190j
0.022727272727272727273 + 1.3118994344635350611e-875j 1.55e-74, 1.62e-190j
0.022727272727272727273 - 5.1730914102796546051e-876j 4.81e-76, 5.02e-192j
0.022727272727272727273 - 8.4156663497513772734e-878j 2.8e-75, 2.92e-191j
0.022727272727272727273 + 5.0634423476389052294e-877j 2.58e-77, 2.69e-193j
0.022727272727272727273 - 1.1647405111080894405e-876j 7.6e-80, 7.93e-196j
0.022727272727272727273 - 2.8381572318239590672e-876j 1.23e-79, 1.28e-195j
0.022727272727272727273 + 4.5883635065175220963e-876j 9.36e-78, 9.76e-194j
0.022727272727272727273 - 1.0085713006694720034e-875j 3.58e-76, 3.73e-192j
0.022727272727272727273 + 1.2547280997564095859e-876j 1.12e-80, 1.17e-196j
0.022727272727272727273 - 7.0336021169760141336e-877j 2.74e-80, 2.86e-196j
0.022727272727272727273 + 2.6365391693029601822e-877j 2.68e-77, 2.79e-193j
0.022727272727272727273 + 3.7154413795007416863e-876j 1.4e-79, 1.46e-195j
0.022727272727272727273 - 4.1119977300821594803e-876j 7.12e-79, 7.43e-195j
0.022727272727272727273 + 1.4508651003687473879e-876j 3.11e-82, 3.24e-198j
0.022727272727272727273 + 6.3587558248267461663e-877j 2.3e-80, 2.4e-196j
0.022727272727272727273 - 5.7028058150949337247e-877j 7.02e-80, 7.32e-196j
0.022727272727272727273 - 1.7983074036252322848e-876j 1.13e-83, 1.18e-199j
0.022727272727272727273 - 3.3793626437987626236e-876j 2.2e-81, 2.3e-197j
0.022727272727272727273 + 2.2404848514679078552e-876j 8.29e-84, 8.64e-200j
0.022727272727272727273 + 9.1987863511222841654e-877j 9.14e-84, 9.53e-200j
0.022727272727272727273 + 7.7299185096971260122e-877j 8.98e-83, 9.37e-199j
0.022727272727272727273 - 1.5585772171644672996e-876j 1.99e-84, 2.08e-200j
0.022727272727272727273 - 2.4181627736967891273e-876j 1.47e-84, 1.53e-200j
0.022727272727272727273 + 2.6159754192810539013e-876j 2.13e-84, 2.22e-200j
0.022727272727272727273 + 1.6739956988446303454e-876j 2.78e-85, 2.9e-201j
0.022727272727272727273 - 8.4505753438413822429e-877j 2.12e-85, 2.22e-201j
0.022727272727272727273 - 1.3498631446765485446e-876j 1.47e-85, 1.54e-201j
0.022727272727272727273 - 2.0796231830575077237e-876j 4.33e-86, 4.52e-202j
0.022727272727272727273 + 3.0902004759820702508e-876j 4.24e-86, 4.42e-202j
0.022727272727272727273 + 1.9329391692472397356e-876j 3.73e-86, 3.89e-202j
0.022727272727272727273 + 1.0792819253101171203e-876j 1.89e-87, 1.97e-203j
0.022727272727272727273 - 9.9781689327119347935e-877j 1.71e-87, 1.78e-203j

Download

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