Rule: Q[2, 6, 18]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{26}-\frac{24516004014371226905143525}{2272458258739826193262772}\cdot t^{24}+\frac{41808543066376067434493895675}{1211220251908327361009057476}\cdot t^{22}-\frac{1601193989682126500758170265925}{24743499431841544660613602724}\cdot t^{20}+\frac{216406397377752248654653917711025}{2746528436934411457328109902364}\cdot t^{18}-\frac{104549118403227731747727231264600}{1602141588211740016774730776379}\cdot t^{16}+\frac{1318796740797867615374295818082975}{35247114940658280369044077080338}\cdot t^{14}-\frac{5741726638553301227618915418175}{387330933413827256802682165718}\cdot t^{12}+\frac{440785467665159013586361125753725}{110794252907873405775421766766517}\cdot t^{10}-\frac{3455625613213688655736239979925}{4979516984623523855075135585012}\cdot t^8+\frac{338596566399496219366208198903}{4632512316705508255418331711492}\cdot t^6-\frac{257549464917181923272887335595}{63311001661641946157383866723724}\cdot t^4+\frac{1355710879858116415961576105}{14938550953870571565225406755036}\cdot t^2-\frac{4791398699021968260548525}{13946129736655393733969173439142}$

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.