Rule: Q[1, 4, 6, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{11}-\frac{319}{117}\cdot t^9+\frac{15994}{5915}\cdot t^7-\frac{219098}{186745}\cdot t^5+\frac{23263}{112047}\cdot t^3-\frac{383}{37349}\cdot t$
• $P_4$:
  $t^{23}-\frac{26344210519069911605394400164148831}{4424903245210860863744756348342925}\cdot t^{21}+\frac{6219722870443781394948058496724130247}{402666195314188338600772827699206175}\cdot t^{19}-\frac{30567257409937313125240661237286857030839}{1334838437466534342461561923822868470125}\cdot t^{17}+\frac{5034943478580557286358992586385705908694}{235559724258800178081452104204035612375}\cdot t^{15}-\frac{124767369874916774325656989203834035681182}{9563724804907287230106955430683845862425}\cdot t^{13}+\frac{1791219898380616736134027534291456615630826}{342087079560145273999979559635999102002125}\cdot t^{11}-\frac{1389920235509298951846597182689125316085146}{1026261238680435821999938678907997306006375}\cdot t^9+\frac{857353392452625131178835238867255707468801}{3991015928201694863333094862419989523358125}\cdot t^7-\frac{401342889142356130478333836165069520231}{21116486392601560123455528372592537160625}\cdot t^5+\frac{4532086959759134845315673399566021327009}{5815480352522469657999652513811984734036125}\cdot t^3-\frac{18374728048950775644657398002257504809}{1938493450840823219333217504603994911345375}\cdot t$

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.