Rule: Q[14, 15]

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.

• $P_1$:
  $\frac{5014575}{2048}\cdot t^{14}-\frac{16900975}{2048}\cdot t^{12}+\frac{22309287}{2048}\cdot t^{10}-\frac{14549535}{2048}\cdot t^8+\frac{4849845}{2048}\cdot t^6-\frac{765765}{2048}\cdot t^4+\frac{45045}{2048}\cdot t^2-\frac{429}{2048}$
• $P_2$:
  $\frac{5014575}{2048}\cdot t^{29}-\frac{1125679225}{63488}\cdot t^{27}+\frac{1246045465377}{21649408}\cdot t^{25}-\frac{47214967905675}{427083776}\cdot t^{23}+\frac{8279453236577043825}{59273676019712}\cdot t^{21}-\frac{265097233046280722625}{2171571948722176}\cdot t^{19}+\frac{176605704398010038878576125}{2337777550961525184512}\cdot t^{17}-\frac{726057371676924810034804575}{21792010317704287209472}\cdot t^{15}+\frac{178061417637221459917825875}{17122293821053368521728}\cdot t^{13}-\frac{3503109277026088716043125}{1556572165550306229248}\cdot t^{11}+\frac{506427460349983422173415}{1556572165550306229248}\cdot t^9-\frac{45984186886513366599795}{1556572165550306229248}\cdot t^7+\frac{1182006318122506084941}{778286082775153114624}\cdot t^5-\frac{198656712028989477405}{5448002579426071802368}\cdot t^3+\frac{708641731665230805}{2724001289713035901184}\cdot t$

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.