Rule: Q[2, 6, 8, 9]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{16}-\frac{52675}{9724}\cdot t^{14}+\frac{62424565}{7972932}\cdot t^{12}-\frac{25786918405}{4472814852}\cdot t^{10}+\frac{2493674299078805}{1096541870671764}\cdot t^8-\frac{66130895817287}{143027200522404}\cdot t^6+\frac{613871878555495}{14255044318732932}\cdot t^4-\frac{244523487906245}{156805487506062252}\cdot t^2+\frac{24672636591575}{1411249387554560268}$
• $P_4$:
  $\frac{3}{2}\cdot t^{25}-\frac{584523165633859525}{63180215311321108}\cdot t^{23}+\frac{167334605536244975937660256823887775}{6678487419043957556794667094466284}\cdot t^{21}-\frac{339864710171550572231717786035112237930954924065193825}{8678339962862348331702135343409160429238261070528802}\cdot t^{19}+\frac{35826509074534281098632900190807753048484396272707601108993630240901175}{917347051993620131502905969471039238979679558217010170528401581847646}\cdot t^{17}-\frac{171370269235978238184440988698990454406035686681998204347624982867541}{6607541791070493144078554401952263426024102460146531840540707672372}\cdot t^{15}+\frac{486264623453834570204540248153046263810475266264123629907327726654685}{41847764676779789912497511212364335031485982247594701656757815258356}\cdot t^{13}-\frac{138959729803912057539762893485745963424361919307445075900755369160927655}{39906672207541465811171665115360050875794747840263962802986664289064564}\cdot t^{11}+\frac{13549715375656597170838726428282238195434415490697393204889097471195155}{20011850285893227723490776348171755717773905808460814191527036930879884}\cdot t^9-\frac{6740079994720294366048428575031448709088848801019603303992607939798755}{83700357941791515954600310599099327486244828262371818086783717956934118}\cdot t^7+\frac{441565208444592521617246524901211897227025553595868752136940045130925}{83700357941791515954600310599099327486244828262371818086783717956934118}\cdot t^5-\frac{7260713841919137872400785161041807798354688352785996155829631720429725}{45700395436218167711211769587108232807489676231255012675383910004486028428}\cdot t^3+\frac{12979947803132664054217235065661546247036198481474345524396828431125}{7979434123784124521005229610447469220355340294346113324273381111894385916}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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