Rule: Q[1, 42]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{43}-\frac{903}{85}\cdot t^{41}+\frac{74046}{1411}\cdot t^{39}-\frac{6096454}{38097}\cdot t^{37}+\frac{112784399}{334407}\cdot t^{35}-\frac{112784399}{216381}\cdot t^{33}+\frac{902275192}{1475325}\cdot t^{31}-\frac{3995790136}{7179915}\cdot t^{29}+\frac{202786349402}{509773965}\cdot t^{27}-\frac{2636222542226}{11724801195}\cdot t^{25}+\frac{5272445084452}{52370778671}\cdot t^{23}-\frac{405572698804}{11384951885}\cdot t^{21}+\frac{202786349402}{20492913393}\cdot t^{19}-\frac{296380049126}{138896412997}\cdot t^{17}+\frac{2879120477224}{8194888366823}\cdot t^{15}-\frac{1060728596872}{24584665100469}\cdot t^{13}+\frac{1723683969917}{450718860175265}\cdot t^{11}-\frac{101393174701}{434329083441619}\cdot t^9+\frac{202786349402}{22150783255522569}\cdot t^7-\frac{1524709394}{7383594418507523}\cdot t^5+\frac{762354697}{347028937669853581}\cdot t^3-\frac{762354697}{109314115366003878015}\cdot t$

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.