Rule: Q[1, 2, 46]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{49}-\frac{364937148433476606323}{30178539594261089130}\cdot t^{47}+\frac{10135676284296339348929}{147716009592962173110}\cdot t^{45}-\frac{577287772887762794291}{2377703119547843386}\cdot t^{43}+\frac{3939584551088517326256485}{6560082906832499901974}\cdot t^{41}-\frac{629623051072700783088020597}{570727212894427491471738}\cdot t^{39}+\frac{102192372627814120778329609}{65468033867781831005530}\cdot t^{37}-\frac{9461725953025517421994964703}{5433846811025891973458990}\cdot t^{35}+\frac{2683501798843043311231749427}{1726045457619989215098738}\cdot t^{33}-\frac{293033653216756929262133425}{261221438988465800752491}\cdot t^{31}+\frac{1446380147008139869065629831}{2199315986322244322464521}\cdot t^{29}-\frac{1785452353799887636859202613}{5687886171523045661546175}\cdot t^{27}+\frac{20616515535940533997648943173}{169161947990111320971169575}\cdot t^{25}-\frac{18421283559168375682516050961}{480419932291916151558121593}\cdot t^{23}+\frac{1272281242346655822932033005}{131023617897795314061305889}\cdot t^{21}-\frac{5734197075512662453193624393}{2926194133050762014035831521}\cdot t^{19}+\frac{19704478509014566922759525092}{63400872882766510304109682955}\cdot t^{17}-\frac{2552051083901213291565279097}{67130335993517481498469076070}\cdot t^{15}+\frac{16228694545791982923799112423}{4640943895018508554260828792306}\cdot t^{13}-\frac{14765206561277210713710517615}{63188236109098154931089745864474}\cdot t^{11}+\frac{38928616086145545518668053991}{3601729458218594831072115514275018}\cdot t^9-\frac{33951163480317850603446967}{105313726848496924885149576440790}\cdot t^7+\frac{11095341391365032786713337}{2000960810121441572817841952375010}\cdot t^5-\frac{535992256348540611645224437}{11898913553468164456918578953993234466}\cdot t^3+\frac{433247402014982250309545}{3966304517822721485639526317997744822}\cdot t$

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.