Rule: Q[1, 2, 10, 14]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{13}-\frac{124943}{42780}\cdot t^{11}+\frac{576433}{179676}\cdot t^9-\frac{310453}{189658}\cdot t^7+\frac{10439}{27094}\cdot t^5-\frac{97669}{2763588}\cdot t^3+\frac{3421}{4605980}\cdot t$
• $P_4$:
  $t^{27}-\frac{6014454661153989176140823607177861773681}{948587122317463049319117986012804595510}\cdot t^{25}+\frac{1947138995429499488892496559600587928238805}{109783149622874390241199254914548585187024}\cdot t^{23}-\frac{2045184859177756229297903046469122042065045615}{71010605084326187113840057189727795731624176}\cdot t^{21}+\frac{101636424981055232682941564360236512460136665}{3381457384967913672087621770939418844363056}\cdot t^{19}-\frac{183121863422840642885319695015374073606958912325}{8686252136217313820714766093381063975622509168}\cdot t^{17}+\frac{8876645470721717884252274960212470737303437692355}{879099811785993436972926768450712974709325119032}\cdot t^{15}-\frac{27953031755941175885755516543811890893515189842325}{8497964847264603224071625428356892088856809483976}\cdot t^{13}+\frac{54508167437499788265232141696806893670948234369475}{76481683625381429016644628855212028799711285355784}\cdot t^{11}-\frac{494708867785215981425434709678971914520354841981}{5034844376592507866299489673854083400607952954456}\cdot t^9+\frac{5958182066971524276339835902152881127468612003357}{746275822041600610404835469435705250712334360138256}\cdot t^7-\frac{59349905617437372548514211668095053166542769413}{177684719533714431048770349865644107312460561937680}\cdot t^5+\frac{33334271620179050690240741477463546794007133289}{6076817408053033541867945965405028470086151218268656}\cdot t^3-\frac{548520859799896464091641277872978292792453907}{34435298645633856737251693803961827997154856903522384}\cdot t$

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.