Rule: Q[14, 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.

• $P_1$:
  $\frac{5014575}{2048}\cdot t^{14}-\frac{16900975}{2048}\cdot t^{12}+\frac{22309287}{2048}\cdot t^{10}-\frac{14549535}{2048}\cdot t^8+\frac{4849845}{2048}\cdot t^6-\frac{765765}{2048}\cdot t^4+\frac{45045}{2048}\cdot t^2-\frac{429}{2048}$
• $P_2$:
  $\frac{5014575}{2048}\cdot t^{30}-\frac{1125679225}{63488}\cdot t^{28}+\frac{1246045465377}{21649408}\cdot t^{26}-\frac{47214967905675}{427083776}\cdot t^{24}+\frac{8279453236577043825}{59273676019712}\cdot t^{22}-\frac{265097233046280722625}{2171571948722176}\cdot t^{20}+\frac{176605704398010038878576125}{2337777550961525184512}\cdot t^{18}-\frac{726057371676924810034804575}{21792010317704287209472}\cdot t^{16}+\frac{408881368963226674314966702481875}{39317820567521923816232876032}\cdot t^{14}-\frac{972372203030901002393719292625}{432063962280460701277284352}\cdot t^{12}+\frac{311688008849533074398432775}{958013220134059204605952}\cdot t^{10}-\frac{1160376599085174624439089855}{39278542025496427388844032}\cdot t^8+\frac{59657370593305414314756663}{39278542025496427388844032}\cdot t^6-\frac{10030090644588215767730265}{274949794178474991721908224}\cdot t^4+\frac{71779444292607314301405}{274949794178474991721908224}\cdot t^2-\frac{2399833002338835885}{274949794178474991721908224}$

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.