Rule: Q[1, 2, 8, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{23}-\frac{25371865499281358445058517}{4121221662869825874849645}\cdot t^{21}+\frac{231912954872273254521412163}{14012153653757407974488793}\cdot t^{19}-\frac{469879528152004709122728113}{18437044281259747334853675}\cdot t^{17}+\frac{2826135089590126238906636550434}{114074331096220235524818476325}\cdot t^{15}-\frac{120137760916109237312663000174}{7604955406414682368321231755}\cdot t^{13}+\frac{175012647587378460807807295394}{26324845637589285121111956075}\cdot t^{11}-\frac{5720536582515902443512609734}{3158981476510714214533434729}\cdot t^9+\frac{13341170441193955223008654817}{43874742729315475201853260125}\cdot t^7-\frac{23895958931558081234811401611}{833620111856994028835211942375}\cdot t^5+\frac{631561618372486948220183263}{500172067114196417301127165425}\cdot t^3-\frac{47266142630959591500805357}{2834308380313779698039720604075}\cdot t$

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.