Rule: Q[1, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{27}-\frac{566849699789789}{86119620555591}\cdot t^{25}+\frac{2903299997774762950}{150918483622204971}\cdot t^{23}-\frac{2189469268913466361250}{66555051277392392211}\cdot t^{21}+\frac{261858003696446239225}{7172599511097425727}\cdot t^{19}-\frac{2702153023549236384985}{98025526651664818269}\cdot t^{17}+\frac{4245848944532369678020}{294076579954994454807}\cdot t^{15}-\frac{19040696688683096722900}{3626944486111598275953}\cdot t^{13}+\frac{127928939774368035875}{98025526651664818269}\cdot t^{11}-\frac{2334106173418924794175}{10880833458334794827859}\cdot t^9+\frac{5768396820774095989910}{262348984495405608627267}\cdot t^7-\frac{4141407113959319988290}{3260623093014326850081747}\cdot t^5+\frac{97114360141529503175}{2839897532625381450071199}\cdot t^3-\frac{195956138132076425}{715746532612901015871603}\cdot t$

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.