Rule: Q[2, 3, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{11}-\frac{2114365}{488852}\cdot t^9+\frac{2243043}{488852}\cdot t^7-\frac{1964259}{907868}\cdot t^5+\frac{386565}{907868}\cdot t^3-\frac{11007}{453934}\cdot t$
• $P_4$:
  $\frac{3}{2}\cdot t^{23}-\frac{61063416600643794465398096623320612819571093}{6495551261197576574180955878106797013407828}\cdot t^{21}+\frac{23929919338399002445298610727726919043064223}{927935894456796653454422268300971001915404}\cdot t^{19}-\frac{1837982315060261856054590505598804339984753483}{45236874854768836855903085579672336343375945}\cdot t^{17}+\frac{647286252622659309781469032004885463625557533}{15965955831094883596201089028119648121191510}\cdot t^{15}-\frac{1233285985756092975940770357773431592432661179}{46301271910175162428983158181546979551455379}\cdot t^{13}+\frac{32026095924997892515006578134805604823917277933}{2760268133106596221727842122361454550182916825}\cdot t^{11}-\frac{32683730703387740208095627870562251529581956273}{9936965279183746398220231640501236380658500570}\cdot t^9+\frac{11180516634668311537351240206143219541372488321}{19321876931746173552094894856530181851280417775}\cdot t^7-\frac{48944570224370587707299400041904434491643903}{849313271725106529762412960726601400056282100}\cdot t^5+\frac{61038701185756997066654759321217650959130149}{22523787966149825169299191718469469129492601292}\cdot t^3-\frac{3634340718023576869391528298569152823128069}{93849116525624271538746632160289454706219172050}\cdot t$

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.