Rule: Q[3, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^7-\frac{77}{18}\cdot t^5+\frac{3745}{1782}\cdot t^3-\frac{155}{594}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{21}-\frac{3154018538165635741}{246284005254113214}\cdot t^{19}+\frac{7892072105177104337036}{280394339981807894139}\cdot t^{17}-\frac{265924088583647259325133}{7669609887737686516155}\cdot t^{15}+\frac{388996810415054045638616}{14827912449626193931233}\cdot t^{13}-\frac{57794390155467624793862}{4601765932642611909693}\cdot t^{11}+\frac{137437135124485251291691}{36395785103627930558481}\cdot t^9-\frac{317853133842850693417187}{465057254101912446025035}\cdot t^7+\frac{11707428706438598797703}{172243427445152757787050}\cdot t^5-\frac{8607252137819757485089}{2790343524611474676150210}\cdot t^3+\frac{10358916317135083061}{255031397410726180078245}\cdot t$

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.