Rule: Q[1, 6, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^7-\frac{21}{13}\cdot t^5+\frac{105}{143}\cdot t^3-\frac{35}{429}\cdot t$
• $P_3$:
  $t^{29}-\frac{1278741772381889563901}{183579225274692011349}\cdot t^{27}+\frac{2624601410770074272136}{120817096975652007469}\cdot t^{25}-\frac{147998810268036918599083525}{3696640716164024472528993}\cdot t^{23}+\frac{146579561143861505016632050}{3024524222316020022978267}\cdot t^{21}-\frac{250866456954793253297997440}{6193073407599469570860261}\cdot t^{19}+\frac{17013668097307799510100655}{711249326923188382087593}\cdot t^{17}-\frac{1949017840539616958509849690}{194171066250030428309912889}\cdot t^{15}+\frac{192123935535089937105472975}{64723688750010142769970963}\cdot t^{13}-\frac{3011066929867824367109975}{4978745288462318674613151}\cdot t^{11}+\frac{8521001887978712361156730}{104553651057708692166876171}\cdot t^9-\frac{90424934073593574332862785}{13324781973687985546156329793}\cdot t^7+\frac{41300317349981705355580}{132805135950378593483285679}\cdot t^5-\frac{1529203909529415694219850}{242293484460326431053577343787}\cdot t^3+\frac{249576889875869727625225}{7349569028629901741958512761539}\cdot t$

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.