Rule: Q[2, 6, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{24}-\frac{1696208257118225132570671}{182525976695021167453388}\cdot t^{22}+\frac{201556972700422528812145173}{7981363162755016504098148}\cdot t^{20}-\frac{433883418106971482809874802297}{10974374348788147693134953500}\cdot t^{18}+\frac{4753651677239104417949009449529}{120718117836669624624484488500}\cdot t^{16}-\frac{313847930600209393218403163961}{12071811783666962462448448850}\cdot t^{14}+\frac{10675948929902245175047258173}{928600906435920189419111450}\cdot t^{12}-\frac{2963100634181409520342865213}{881326678471909707048683958}\cdot t^{10}+\frac{594385796137916648362273892012}{948650244188513920781569538125}\cdot t^8-\frac{263011497943900658096197632901}{3794600976754055683126278152500}\cdot t^6+\frac{825715908535309817788472353}{206978235095675764534160626500}\cdot t^4-\frac{68820231214330004713957019}{758920195350811136625255630500}\cdot t^2+\frac{4023570156205341878629}{11675695313089402101927009700}$

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.