Rule: Q[1, 2, 4, 14]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{21}-\frac{3154018538165635741}{615710013135283035}\cdot t^{19}+\frac{15784144210354208674072}{1401971699909039470695}\cdot t^{17}-\frac{531848177167294518650266}{38348049438688432580775}\cdot t^{15}+\frac{777993620830108091277232}{74139562248130969656165}\cdot t^{13}-\frac{115588780310935249587724}{23008829663213059548465}\cdot t^{11}+\frac{274874270248970502583382}{181978925518139652792405}\cdot t^9-\frac{635706267685701386834374}{2325286270509562230125175}\cdot t^7+\frac{11707428706438598797703}{430608568612881894467625}\cdot t^5-\frac{8607252137819757485089}{6975858811528686690375525}\cdot t^3+\frac{20717832634270166122}{1275156987053630900391225}\cdot t$

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.