Rule: Q[3, 8, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{11}-\frac{10483}{1482}\cdot t^9+\frac{1617}{221}\cdot t^7-\frac{69993}{20995}\cdot t^5+\frac{68299}{109174}\cdot t^3-\frac{3633}{109174}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{23}-\frac{25371865499281358445058517}{1648488665147930349939858}\cdot t^{21}+\frac{1159564774361366272607060815}{28024307307514815948977586}\cdot t^{19}-\frac{469879528152004709122728113}{7374817712503898933941470}\cdot t^{17}+\frac{1413067544795063119453318275217}{22814866219244047104963695265}\cdot t^{15}-\frac{60068880458054618656331500087}{1520991081282936473664246351}\cdot t^{13}+\frac{87506323793689230403903647697}{5264969127517857024222391215}\cdot t^{11}-\frac{14301341456289756108781524335}{3158981476510714214533434729}\cdot t^9+\frac{13341170441193955223008654817}{17549897091726190080741304050}\cdot t^7-\frac{23895958931558081234811401611}{333448044742797611534084776950}\cdot t^5+\frac{631561618372486948220183263}{200068826845678566920450866170}\cdot t^3-\frac{47266142630959591500805357}{1133723352125511879215888241630}\cdot t$

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.