Rule: Q[2, 6, 23]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{31}-\frac{8173315889517809953573279867891468303}{705229703423670368169904435795320868}\cdot t^{29}+\frac{364011172940591415287076692503292293687}{8991678718651797194166281556390341067}\cdot t^{27}-\frac{1500327531475534437313599362645026506950}{17752801572722779075661632816462981081}\cdot t^{25}+\frac{391936535850957127758349899072329154421175}{3337526695671882466224386969495040443228}\cdot t^{23}-\frac{11165170166163258384547217490342938850890}{97525130717684877259803515342387545419}\cdot t^{21}+\frac{449612600799726971093794637284620208114415}{5591440827813932962895401546296885937356}\cdot t^{19}-\frac{1157924149289402094914428053094208515104415}{28153395045308750181596144627845723930196}\cdot t^{17}+\frac{4662229358245220118750589977354324298300}{304656605651232313285862830323524759511}\cdot t^{15}-\frac{12588417408976628048806925767038464914425}{3075580971336250019838234287075583286492}\cdot t^{13}+\frac{636209965648939680248132386264355650955}{828041030744375005341063077289580115594}\cdot t^{11}-\frac{8942766824321485383821463352932451378945}{91912554412625625592858001579143392830934}\cdot t^9+\frac{68290665724167403358613134601257313415}{8753576610726250056462666817061275507708}\cdot t^7-\frac{1560791818662669086901785798409483175}{4376788305363125028231333408530637753854}\cdot t^5+\frac{1812357952997487761588512376630972648725}{236582915058098360276016496064715093146824116}\cdot t^3-\frac{3880906273048084901684029661853138625}{78860971686032786758672165354905031048941372}\cdot t$

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.