Rule: Q[15, 16]

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.

• $P_1$:
  $\frac{9694845}{2048}\cdot t^{15}-\frac{35102025}{2048}\cdot t^{13}+\frac{50702925}{2048}\cdot t^{11}-\frac{37182145}{2048}\cdot t^9+\frac{14549535}{2048}\cdot t^7-\frac{2909907}{2048}\cdot t^5+\frac{255255}{2048}\cdot t^3-\frac{6435}{2048}\cdot t$
• $P_2$:
  $\frac{9694845}{2048}\cdot t^{31}-\frac{825621915}{22528}\cdot t^{29}+\frac{222272849551}{1734656}\cdot t^{27}-\frac{566430703519519}{2118014976}\cdot t^{25}+\frac{11800132631055228101}{31801994864640}\cdot t^{23}-\frac{419447632808062185469}{1162921595996160}\cdot t^{21}+\frac{19942408194939963739082185061}{79068649958189373081600}\cdot t^{19}-\frac{334577379775286607276883763489}{2609265448620249311692800}\cdot t^{17}+\frac{87168445597121055316840245364351511}{1841371673418553040508167424000}\cdot t^{15}-\frac{219893689975630508963208782260699}{17536873080176695623887308800}\cdot t^{13}+\frac{3138076942054090166951284270711}{1348990236936668894145177600}\cdot t^{11}-\frac{961820275632644204108024748683}{3311157854299096376538163200}\cdot t^9+\frac{8428295386676143362626190367}{367906428255455152948684800}\cdot t^7-\frac{9445174288403354543155875283}{9197660706386378823717120000}\cdot t^5+\frac{118942299923828033141748437}{5518596423831827294230272000}\cdot t^3-\frac{1733306412821452272865021}{12876724988940930353203968000}\cdot t$

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.