Rule: Q[2, 37]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{39}-\frac{719337143179}{50921776010}\cdot t^{37}+\frac{1138882587206517}{18586448243650}\cdot t^{35}-\frac{6120390042446661}{37703937865690}\cdot t^{33}+\frac{127316465995907298}{433595285455435}\cdot t^{31}-\frac{485154115147516914}{1263081918500615}\cdot t^{29}+\frac{141784104380718604266}{377661493631683885}\cdot t^{27}-\frac{40578338118322482786}{145254420627570725}\cdot t^{25}+\frac{396410479261033767651}{2480945504318907983}\cdot t^{23}-\frac{7597424653628052969}{107867195839952521}\cdot t^{21}+\frac{21683916434395443327}{909166364936742677}\cdot t^{19}-\frac{5589532114854124779}{909166364936742677}\cdot t^{17}+\frac{286179231557916214614}{240929086708236809405}\cdot t^{15}-\frac{8096507554684875606}{48185817341647361881}\cdot t^{13}+\frac{93011732328260574}{5529520022811992347}\cdot t^{11}-\frac{1878367983995698074}{1656297572206177230029}\cdot t^9+\frac{10607594094014356989}{221943874675627748823886}\cdot t^7-\frac{7614814142874297249}{6816847579322852285305070}\cdot t^5+\frac{652220715343207527}{55898150150447388739501574}\cdot t^3-\frac{24123735282476247}{726675951955816053613520462}\cdot t$

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.