Rule: Q[8, 25]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{33}-\frac{1302401173216935156575483559}{3250560482856624578489968}\cdot t^{31}+\frac{620220474364585602407474619}{427705326691661128748680}\cdot t^{29}-\frac{19015237966912220800808631141837}{6029789695699038593098890640}\cdot t^{27}+\frac{3202928272664818981637891540046875}{697043688822808861362231757984}\cdot t^{25}-\frac{80876134848837991378988864563220145}{17077570376158817103374678070608}\cdot t^{23}+\frac{25458435016424572967270151975410550}{7166480425709503605880445261773}\cdot t^{21}-\frac{676202639877350755493496341503282663}{343991060434056173082261372565104}\cdot t^{19}+\frac{835175722047566990471934913939943793}{1038008112186976522283315018968384}\cdot t^{17}-\frac{3694287450718187377339263124795935}{15264825179220242974754632631888}\cdot t^{15}+\frac{401865550092720273856389364079215}{7632412589610121487377316315944}\cdot t^{13}-\frac{4555009796319043230131665408354935}{564798531631148990065921407379856}\cdot t^{11}+\frac{270337737025145432959881723180735141}{324194357156279520297838887836037344}\cdot t^9-\frac{1262675065766949083763709233820639}{23156739796877108592702777702574096}\cdot t^7+\frac{11741966104342078830444305734245}{5789184949219277148175694425643524}\cdot t^5-\frac{819948812766413430014884841115}{23156739796877108592702777702574096}\cdot t^3+\frac{309207826346099922186836005715}{1667285265375151818674599994585334912}\cdot t$

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.