Rule: Q[1, 2, 4, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{29}-\frac{743669323805712117007731327878993851}{101118245240258330221759722752299185}\cdot t^{27}+\frac{2093043399568603222966332551841507719066536}{86168822745693298423444543580876521190415}\cdot t^{25}-\frac{22132943513633149981940009626630315421354495}{465311642826743811486600535336733214428241}\cdot t^{23}+\frac{1098833941924056513364715385309665660888790100}{17893347719610239296257456949767104518467813}\cdot t^{21}-\frac{106022718058073173384810274439914911965506720}{1928355769281303984308447741453597730060441}\cdot t^{19}+\frac{7741361942670806160233913306240929327000317}{221463827844631550018617247617920187485933}\cdot t^{17}-\frac{73902727576746122749200976845259470123008158}{4650740384737262550390962199976323937204593}\cdot t^{15}+\frac{294335008445275793053732842003993594199657735}{57359131411759571454821867133041328558856647}\cdot t^{13}-\frac{463263595918369303494333342496043493173980475}{401513919882317000183753069931289299911996529}\cdot t^{11}+\frac{209769159109345367116192160910198730071018550}{1204541759646951000551259209793867899735989587}\cdot t^9-\frac{68884619114206275809935308325418209613772239}{4148977172117275668565448389289989432423964133}\cdot t^7+\frac{1603943950950123049099376000379628182134554}{1778133073764546715099477881124281185324556057}\cdot t^5-\frac{1739971014375660508570715921009942044763990}{75443646129724339197792132956273073148770449847}\cdot t^3+\frac{143417554162634120678420206473856774015}{811222001394885367718194978024441646760972579}\cdot t$

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.