Rule: Q[1, 2, 8, 24]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{11}-\frac{10483}{3705}\cdot t^9+\frac{3234}{1105}\cdot t^7-\frac{139986}{104975}\cdot t^5+\frac{68299}{272935}\cdot t^3-\frac{3633}{272935}\cdot t$
• $P_4$:
  $t^{35}-\frac{78351457376627706924051418239660072311672526283713276851}{8257723960747620762073029693724422914550251950306949685}\cdot t^{33}+\frac{2159173740418645084671861426434810194684311662214918370008}{52298918418068264826462521393588011792151595685277348005}\cdot t^{31}-\frac{25533980800028229707271883115579838973043299338247016924504}{233968845554515921592069174655525315912257138592030241075}\cdot t^{29}+\frac{39923249915836265385219394455161212495240975629539758308246453148}{203988218066467584108814385856671095246450056207130641201794145}\cdot t^{27}-\frac{186591043371986947239562002211303049337827538121885513757714306388}{740982843403835241420906957171668508373857041778038653938141125}\cdot t^{25}+\frac{348165841515695486029313901171940670420733120337297810480602786216}{1452326373071517073184977636056470276412759801884955761718756605}\cdot t^{23}-\frac{88091116375357946507543900460157199368251205490232335116652212808}{513228116799709040899954502967324082642103087884157299253996695}\cdot t^{21}+\frac{47738141557522707553052821562211173241802393498638564543144809034}{513228116799709040899954502967324082642103087884157299253996695}\cdot t^{19}-\frac{12636921961842000500325216939517530470339968613194906990432722}{331757024434201060698095994161166181410538518347871557371685}\cdot t^{17}+\frac{1537982623299032081384444457109689110636016065917981262712397416}{131679304060000442283467675980352236472629703399564763888697525}\cdot t^{15}-\frac{107252721503752614519804516617704700063144812193291068304139517176}{40701298300804607295453485306256403633475296440197235784091177345}\cdot t^{13}+\frac{837765368425833122162543451264175886548930479738558521014953479676}{1969316663938930614526172481356559837342766266221850869861026965385}\cdot t^{11}-\frac{1947669031644758253345317645977278512219335177110611002398137328692}{41355649942717542905049622108487756584198091590658868267081566273085}\cdot t^9+\frac{507230499883994096564130531406524179734643202251022976541795736}{151485897226071585732782498565889218257135866632450066912386689645}\cdot t^7-\frac{104068385211756997540900190469645299913199519925513818990726728}{757429486130357928663912492829446091285679333162250334561933448225}\cdot t^5+\frac{5273690797991418402005988805206880191670981093529770559605897}{1969316663938930614526172481356559837342766266221850869861026965385}\cdot t^3-\frac{21215298226446782797527588161855797102226802663824907778593}{1347427191116110420465275908296593572918734813730740068852281607895}\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.