Rule: Q[7, 30]

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.

• $P_1$:
  $\frac{429}{16}\cdot t^7-\frac{693}{16}\cdot t^5+\frac{315}{16}\cdot t^3-\frac{35}{16}\cdot t$
• $P_2$:
  $\frac{429}{16}\cdot t^{37}-\frac{658166866702141218660338941730559681}{2700153475813380598603801405660624}\cdot t^{35}+\frac{17861535372292923886976014456666220775}{17550997592786973890924709136794056}\cdot t^{33}-\frac{45394761358717907436617729793734924725}{17550997592786973890924709136794056}\cdot t^{31}+\frac{4786961887723036791469490922408355465695}{1070610853160005407346407257344437416}\cdot t^{29}-\frac{351514607067000307877821614479474962501197}{63166040336440319033438028183321807544}\cdot t^{27}+\frac{475268100741293786275520855260699503351201}{92319597414797389356563271960239564872}\cdot t^{25}-\frac{332643893214864442701580735747739922754425}{92319597414797389356563271960239564872}\cdot t^{23}+\frac{1176693549051140167204665861978491951916150}{611617332873032704487231676736587117277}\cdot t^{21}-\frac{479785038870245786782627354653310094736900}{611617332873032704487231676736587117277}\cdot t^{19}+\frac{62552392093131484883228111867515442749485}{257523087525487454520939653362773523064}\cdot t^{17}-\frac{682905395696035373187937026971380979531895}{12103585113697910362484163708050355584008}\cdot t^{15}+\frac{116635107482305510744842684624560069834925}{12103585113697910362484163708050355584008}\cdot t^{13}-\frac{14211470636041140283842101387075725545525}{12103585113697910362484163708050355584008}\cdot t^{11}+\frac{14578576618374521793950315869766479443054975}{149370343888145911783417064321049438262242728}\cdot t^9-\frac{189482442322415583352323215717858888419455}{36638008878224468928007959173087598064323688}\cdot t^7+\frac{86893385506112295359496109819860803354565}{554804134441684815195549096049612199259758704}\cdot t^5-\frac{1234255072391729745849772589434198567725}{554804134441684815195549096049612199259758704}\cdot t^3+\frac{1301224695423646475239312229258455575}{138701033610421203798887274012403049814939676}\cdot t$

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.