Rule: Q[8, 18]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{26}-\frac{75523229234793483}{227454293416832}\cdot t^{24}+\frac{131269447510723104363}{135221577436306624}\cdot t^{22}-\frac{1118281326831180707517}{676107887181533120}\cdot t^{20}+\frac{5916289071570332846382131}{3252078937343174307200}\cdot t^{18}-\frac{21982324550946546260931849}{16260394686715871536000}\cdot t^{16}+\frac{6173146862815314252690099}{8943217077693729344800}\cdot t^{14}-\frac{5149433311946782426747731}{21326133031423508437600}\cdot t^{12}+\frac{12743570755797032157318441}{224893766513193361705600}\cdot t^{10}-\frac{1922272710111398807426487}{224893766513193361705600}\cdot t^8+\frac{2160608743522380018607453}{2811172081414917021320000}\cdot t^6-\frac{20227771288499889686019}{562234416282983404264000}\cdot t^4+\frac{745781267930311264071}{1124468832565966808528000}\cdot t^2-\frac{6852688637206535123}{3373406497697900425584000}$

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.