Rule: Q[3, 42]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{45}-\frac{1364494424873097033}{49809029334008456}\cdot t^{43}+\frac{592371541037941974099}{4233767493390718760}\cdot t^{41}-\frac{15543751879381937433159}{35140270195142965708}\cdot t^{39}+\frac{34067737941548007816483}{35140270195142965708}\cdot t^{37}-\frac{8681000880212010151179469}{5552162690832588581864}\cdot t^{35}+\frac{20715890931989077550119667}{10777727576322083717736}\cdot t^{33}-\frac{1878979015566488544980063}{1020618141697167018725}\cdot t^{31}+\frac{20750811437218665668868262}{14901024868778638473385}\cdot t^{29}-\frac{1100875541834706512131224331}{1313345502227524135792140}\cdot t^{27}+\frac{1351617336140718070847573787}{3356327394581450569246580}\cdot t^{25}-\frac{3469354003353593661612425301}{22487393543695718813952086}\cdot t^{23}+\frac{229341461471522554038757327}{4888563813846895394337410}\cdot t^{21}-\frac{21953742236834652585375153}{1955425525538758157734964}\cdot t^{19}+\frac{248991674557471005899677251}{119280957057864247621832804}\cdot t^{17}-\frac{520957222922646321357721921}{1759394116603497652422033859}\cdot t^{15}+\frac{109958329537450938774119337}{3518788233206995304844067718}\cdot t^{13}-\frac{1834549057915189168584112809}{774133411305538967065694897960}\cdot t^{11}+\frac{275173226994428812101319631}{2237949316319649013880827068648}\cdot t^9-\frac{25746134491543097835644259}{6340856396239005539329010027836}\cdot t^7+\frac{482714274462158000246439}{6340856396239005539329010027836}\cdot t^5-\frac{2758171113084521264860483}{4172283508725265644878488598316088}\cdot t^3+\frac{34821925198302866587041}{20861417543626328224392442991580440}\cdot t$

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.