Rule: Q[4, 11, 12]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{15}-\frac{638415}{40664}\cdot t^{13}+\frac{11181153}{503608}\cdot t^{11}-\frac{55088825}{3525256}\cdot t^9+\frac{19993545}{3525256}\cdot t^7-\frac{160318323}{162665384}\cdot t^5+\frac{10517265}{162665384}\cdot t^3-\frac{64053}{91941304}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{27}-\frac{353810850417}{12121572424}\cdot t^{25}+\frac{3301833872910204305109}{38149138589700635420}\cdot t^{23}-\frac{28611196629157957218033741147}{190355966324645394065153900}\cdot t^{21}+\frac{426080704462385735828525471740774809}{2512922015840108535757927896217000}\cdot t^{19}-\frac{3375719083305214612498468225500170864716118907}{25914403110000146287260867281665716337465000}\cdot t^{17}+\frac{13458590033211937809911144048007409262347778977567203}{193689262137860388232229029661832656737072518118750}\cdot t^{15}-\frac{12969393486454616392929736605159443680048259769479193}{503592081558437009403795477120764907516388547108750}\cdot t^{13}+\frac{872353768429709170838906097574569596039145598919787}{133578801474386474642916572180574246025567253875000}\cdot t^{11}-\frac{354955749528553277955262987464789950903376757970617}{323989311212421013043001285979792807632921303035000}\cdot t^9+\frac{5652118946983909749499571179863895098073190449677}{49302721271455371550021934823011948987618459157500}\cdot t^7-\frac{520188378902431254546323392185682554407164812797061}{76947461412949990597712805420200791812818809470812500}\cdot t^5+\frac{375066092552102900339783814477721682170566824889}{2020242230146949560094390258136545885433080711975000}\cdot t^3-\frac{171636020742601294053925130788477767020868116403}{113748421219143464361836321055948996592862587913375000}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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