Rule: Q[1, 2, 10, 26]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{13}-\frac{124943}{42780}\cdot t^{11}+\frac{576433}{179676}\cdot t^9-\frac{310453}{189658}\cdot t^7+\frac{10439}{27094}\cdot t^5-\frac{97669}{2763588}\cdot t^3+\frac{3421}{4605980}\cdot t$
• $P_4$:
  $t^{39}-\frac{3189268649727806706148217532503789540996578918504609895242606216498470312696897712229}{326709098717516490345022306317451218140670640696168101751564365827461218826575283340}\cdot t^{37}+\frac{362053604428936295809194895816122255930082184346298408366715746930109348876889473549597}{8233069287681415556694562119199770697144900145543436164139422018852022714429697140168}\cdot t^{35}-\frac{2537295540237583350702753314868915917397368624191530287005653363624282870239580747283521719651}{20925885178599114062048331509062507583914129816225859633723035132829941056970673635102183416}\cdot t^{33}+\frac{10035776092198633666335305005769425938035235581755959160494975877899421776381595388561364157}{43855755382827071954420700448802498843809806022922908439530373431264795480295174213946747}\cdot t^{31}-\frac{1121529524682451922646552160609112233616144585064075018316722283362713083315817767772359771292}{3580908053694910647714693967205871947190738541698525357525185482902916483928413944773074539}\cdot t^{29}+\frac{1625392153533765844526715361480222701343445380848631767626886196089167348461553277119290399300579}{5058421854980332475836974217152990415835960661729786472434490275631119850558007350681617033570}\cdot t^{27}-\frac{11506883704713101763609293531600386780358456016029149578219536206036498792620126633375642932872291}{45675675860896483615150159783033298643733600345545257110352915896254334058001562670228823436458}\cdot t^{25}+\frac{2574210412274732422852996403918464635328396228750574570072598396136552531257000754879948350340505}{16880141079026961336033754702425349498771113171179768932086947179050514760565794899867173878691}\cdot t^{23}-\frac{354982974609733735522755729276561169471052794587523453581180032488751493863792721329544763215227095}{4962761477233926632793923882513052752638707272326852066033562470640851339606343700560949120335154}\cdot t^{21}+\frac{645361058134531448117623468174809815689833498273822516921500827961546184782920897499404654290265}{24875997379618679863628691140416304524504798357528080531496553737548127015570645115593729926492}\cdot t^{19}-\frac{2814443304681649556164217423210210330683738761961553726072013160838693350835161260773172410138093}{389723958947359317863516161199855437550575174267939928326779341888253989910606773477635102181708}\cdot t^{17}+\frac{1125609785738369864525126771904144791156486428445382414200392754179239456714105985100725672923995}{739329275061902235358729188158549285941532315890650746384625516229187716153945202626690120315299}\cdot t^{15}-\frac{7220864909186383201079497827814697004321986470305104381473151464156143449778572351186282513107810}{30312500277537991649707896714500520723602824951516680601769646165396696362311753307694294932927259}\cdot t^{13}+\frac{1628360240733785100732114211566670568271133490555082060549349619083809615981741025801086503773345}{60625000555075983299415793429001041447205649903033361203539292330793392724623506615388589865854518}\cdot t^{11}-\frac{1140939962799502292705525540744172922936307239972416822774239606657603197594311538230225082093325}{545625004995683849694742140861009373024850849127300250831853630977140534521611559538497308792690662}\cdot t^9+\frac{1315760386381324681402324170769301539664013934020081776460611658606971084159799111948903186076}{12481617761339173032232663353029626180307045568271574365434560185751580855069545479638827325322989}\cdot t^7-\frac{19806986320883464980261857972635738190882566163090352103172393727450660970548718980729500075}{6381579005797471926254294045158004362863752621371932758267293929557199234170895433198798933247844}\cdot t^5+\frac{142432116596925072257887238050383132471452535894900714365213305152585324392209561250559309085}{3221785743784037969626096450798341059765785966275487195388088106722163156222849208703507918585411528}\cdot t^3-\frac{1468590127671433240339249055362483873734540012021200409005972233254725131227934176231931265}{7517500068829421929127558385196129139453500587976136789238872249018380697853314820308185143365960232}\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.