Rule: Q[5, 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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{11}-\frac{2233}{104}\cdot t^9+\frac{71973}{3380}\cdot t^7-\frac{6901587}{746980}\cdot t^5+\frac{488523}{298792}\cdot t^3-\frac{24129}{298792}\cdot t$
• $P_3$:
  $\frac{63}{8}\cdot t^{23}-\frac{184409473633489381237760801149041817}{3933247329076320767773116754082600}\cdot t^{21}+\frac{6219722870443781394948058496724130247}{51132215277992169981050517803073800}\cdot t^{19}-\frac{30567257409937313125240661237286857030839}{169503293646544043487182466517189647000}\cdot t^{17}+\frac{2517471739290278643179496293192852954347}{14956172968812709719457276457399086500}\cdot t^{15}-\frac{62383684937458387162828494601917017840591}{607220622533796014609965424170402911900}\cdot t^{13}+\frac{895609949190308368067013767145728307815413}{21719814575247318984125686326095181079500}\cdot t^{11}-\frac{694960117754649475923298591344562658042573}{65159443725741956952377058978285543238500}\cdot t^9+\frac{857353392452625131178835238867255707468801}{506795673422437442962932680942220891855000}\cdot t^7-\frac{1204028667427068391435001508495208560693}{8044375768610118142268772713368585585000}\cdot t^5+\frac{4532086959759134845315673399566021327009}{738473695558408845460273335087236156703000}\cdot t^3-\frac{18374728048950775644657398002257504809}{246157898519469615153424445029078718901000}\cdot t$

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.