Rule: Q[2, 3, 10, 16]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^5-\frac{25}{14}\cdot t^3+\frac{3}{7}\cdot t$
• $P_3$:
  $\frac{3}{2}\cdot t^{15}-\frac{61157207}{11447800}\cdot t^{13}+\frac{3237322021}{425329800}\cdot t^{11}-\frac{247214528}{44659629}\cdot t^9+\frac{215329367}{99243620}\cdot t^7-\frac{4051191133}{9158768360}\cdot t^5+\frac{5596988947}{137381525400}\cdot t^3-\frac{336966223}{297659971700}\cdot t$
• $P_4$:
  $\frac{3}{2}\cdot t^{31}-\frac{24135998734469238497650064103845586035325060261368670474528478267493770574302188420592742945723389501829}{2110754784762876642301244777525431508566298695531971616511014733990047524462261808447274669092735866600}\cdot t^{29}+\frac{265143374968266426611842735741825043497336618947978146563842767888449749340609911792565564296112882200126799}{6728664102867098160327908101795570563007646981616819119113812769013473498480798192968222190133823395547480}\cdot t^{27}-\frac{5514252298615641237652892833572809903145453323459979339674789334981689811529509908097762742897261181088314779}{67933627961638971811002918335436048953442589718246731491052917379462953590431135602083012496543409281969750}\cdot t^{25}+\frac{1815654980660337645128133589638855185429391054819592194661076004415388912869665033967593728026578424170974909}{16304070710793353234640700400504651748826221532379215557852700171071108861703472544499922999170418227672740}\cdot t^{23}-\frac{1621666666241909906791420362913444806250309045570662048043054657933147649611009929973328257956032998673338111043}{15111746930986639315481323962519920260064234375098265967926254880299734726686722943636928630274564164240324840}\cdot t^{21}+\frac{4882662751458619968661338855730389431558613066436511897740427320096188048806445735458590945789802246805376397}{65418817883059044655763307197055931861749932359732753107905865282682834314661138284142548183006771273767640}\cdot t^{19}-\frac{127407259879347803771211267119948221885429298643500666900979846907384262644860965003751596826419174304236514513997}{3361113848413393014367750261633706926113459768172701915264740667229974457274310486896209054710278344544926084620}\cdot t^{17}+\frac{986075383082418751024160790124119335007019746411593840511286217541941013987261762780243821752604632797591926114123}{70138537513214774814527023842032796002279403103486235555303926570578437571650685013319421303439484866312501677585}\cdot t^{15}-\frac{704824874894669134556629698339676552635173194877571064293632895453828151173895548226800869717735847079758210957949}{187036100035239399505405396912087456006078408275963294814143804188209166857735160035518456809171959643500004473560}\cdot t^{13}+\frac{71917427539808027755830761613668940019434171437247481665630510238522310222633487432080492898117798406072743364027}{100711746172821215118295213721893245541734527533211004899923586870574166769549701557586861358784901346500002408840}\cdot t^{11}-\frac{33505840278406748486808000052783063590301322256698167739850113908498360729623257307894188515968901804958774893}{363531704099755723020584327605764388987544417566403359932879257420521724970299724873642413995613948710628350941}\cdot t^9+\frac{104755493027990407361843472461017893071360756293386203692503758598416793872159639845391157561804411444090586817}{13733419932657438425222074598439988028418344663619682486353216391441931832211322939670935639834304729068182146660}\cdot t^7-\frac{825248345212324203206930002800915399426408766685225089715951766311733576036174637895545156986437612035156819793}{2256204703222293455572197969743712318954442337594662122758028407165460229577574482945939426544207205489772781237000}\cdot t^5+\frac{2692787839934812756934414300530831802040970709729486435955643450941753807667217861779207895662347639529669069}{319970848820616162790238984800017383415357276967970264682047665016192541649183290308696864128087567324004139884520}\cdot t^3-\frac{662726916857432503304523419414504943015340500689767374869296672883663580552866686710291877494229447032276149}{11145651233918129670526657970533938855634945147717630886424660331397373534113217945752940767128383595119477539310780}\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.