Rule: Q[7, 16]

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.

• $P_1$:
  $\frac{429}{16}\cdot t^7-\frac{693}{16}\cdot t^5+\frac{315}{16}\cdot t^3-\frac{35}{16}\cdot t$
• $P_2$:
  $\frac{429}{16}\cdot t^{23}-\frac{814453542657469}{5190588893712}\cdot t^{21}+\frac{332613072544398149}{832224419291824}\cdot t^{19}-\frac{60434669839704081761}{104028052411478000}\cdot t^{17}+\frac{911288943452960320423}{1716462864789387000}\cdot t^{15}-\frac{2788451867710786781}{8802373665586600}\cdot t^{13}+\frac{99305037719399449}{800215787780600}\cdot t^{11}-\frac{3919384318228123579}{125313792366441960}\cdot t^9+\frac{9825341915024369299}{2036020735513470000}\cdot t^7-\frac{44745439665748799999}{107909098982213910000}\cdot t^5+\frac{1067710391708808827}{64745459389328346000}\cdot t^3-\frac{4195757732088601}{21581819796442782000}\cdot t$

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.