Rule: Q[1, 2, 32]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{35}-\frac{2152343575622569}{249276722727135}\cdot t^{33}+\frac{14154197751720488}{415461204545225}\cdot t^{31}-\frac{263651910170873576}{3240597395452755}\cdot t^{29}+\frac{77853958731883336156}{593029323367854165}\cdot t^{27}-\frac{675455917761811956}{4463417537785865}\cdot t^{25}+\frac{145995725803176001368}{1136386105120281229}\cdot t^{23}-\frac{463744498482322187944}{5681930525601406145}\cdot t^{21}+\frac{123731103366294576306}{3169919135335521323}\cdot t^{19}-\frac{44453398252686321822}{3169919135335521323}\cdot t^{17}+\frac{83175453631025061944}{22189433947348649261}\cdot t^{15}-\frac{109069506739834459176}{148986199360769502181}\cdot t^{13}+\frac{75629623583549334572}{744930996803847510905}\cdot t^{11}-\frac{184005018913964215748}{19219219717539265781349}\cdot t^9+\frac{1056162883156588416264}{1838638686311256426415721}\cdot t^7-\frac{5170746937586623272}{262662669473036632345103}\cdot t^5+\frac{40017850937591444159}{126340744016530620157994543}\cdot t^3-\frac{6710008765992630747}{4421926040578571705529809005}\cdot t$

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.