Rule: Q[1, 16, 18]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-\frac{136}{33}\cdot t^{15}+\frac{2380}{341}\cdot t^{13}-\frac{61880}{9889}\cdot t^{11}+\frac{77350}{24273}\cdot t^9-\frac{12376}{13485}\cdot t^7+\frac{43316}{310155}\cdot t^5-\frac{1768}{186093}\cdot t^3+\frac{221}{1178589}\cdot t$
• $P_3$:
  $t^{35}-\frac{10675}{1221}\cdot t^{33}+\frac{19278140}{551707}\cdot t^{31}-\frac{66203873540}{782943421}\cdot t^{29}+\frac{2085364279908280}{15076817481609}\cdot t^{27}-\frac{16704013544994832}{103304119781395}\cdot t^{25}+\frac{61346914499162435101420}{440455730090362189879}\cdot t^{23}-\frac{1336490208409006409952020}{14879743577400496588521}\cdot t^{21}+\frac{206511220996250834249608700570}{4733607088613045433987747109}\cdot t^{19}-\frac{319041703976275751115401512307690}{20030881238504077154634150279511}\cdot t^{17}+\frac{107110622062263444668963992095860}{24744029765210918838077479757043}\cdot t^{15}-\frac{11148263110327593601001814572140}{12961158448443814629469156063213}\cdot t^{13}+\frac{3753418809200989231291680815440}{30907377838596788731811064458431}\cdot t^{11}-\frac{276010516061092581966524646520}{23656380105201647680359788339151}\cdot t^9+\frac{9467698772388128918058609260}{13264688586120820533948511807741}\cdot t^7-\frac{782257906675883145826016284}{31339648857318422140647582842465}\cdot t^5+\frac{7712932001994119458172003}{18803789314391053284388549705479}\cdot t^3-\frac{26350284898247641560823043}{13118777011673491508075078177855849}\cdot t$

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.