Rule: Q[5, 12, 18]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{17}-\frac{15500107}{453038}\cdot t^{15}+\frac{14463685}{235828}\cdot t^{13}-\frac{754990808}{12911583}\cdot t^{11}+\frac{2466422101}{77469498}\cdot t^9-\frac{2971987447}{301270270}\cdot t^7+\frac{61205289431}{37615745140}\cdot t^5-\frac{683012759}{5642361771}\cdot t^3+\frac{39745277}{15046298056}\cdot t$
• $P_3$:
  $\frac{63}{8}\cdot t^{35}-\frac{533877443673504518414311151877141483654845246713007357733056718482701443138127195996061133241462180045}{7378315321173461735803078221908163357319437792033133362735888972659544347671062733393072048319002664}\cdot t^{33}+\frac{79547641748815736345150072716534349655011762238618920230653365734434670428189590847483732182080642868305}{261259437963369395099572633403020875243265547272445949525966250440990229401625357696054687529113776148}\cdot t^{31}-\frac{22539815503148489642992703323717879413768011580750968005672549705553736738932280201243691286095877537869223}{28999797613934002856052562307735317152002475747241500397382253798949915463580414704262070315731629152428}\cdot t^{29}+\frac{366887132849052209339475607220839717011933269617565609418304877699799866867074165748919734920189261006096513}{272998094779447682058701707241784192499885375137825158913288113348735411088188041871156730903266715814236}\cdot t^{27}-\frac{252433570857367480563181925133895320529718747024320319193314537538723756590541560753067774699313979541663657}{151665608210804267810389837356546773611047430632125088285160062971519672826771134372864850501814842119020}\cdot t^{25}+\frac{2469772811346769114082291878910660008082506247786435551458469369209994256761827422109213855534404952017177154945}{1622278344983096167195789400759603163818955599281626365488590484646454897957702865877209630982235382085610436}\cdot t^{23}-\frac{275058381041288609731976741000574552865314363880360859037830859492881806875083294877685495211634669005276022023005}{263161761092692686948151750184090408878631449605206433462518743400692314099138669242950831878031313502670110292}\cdot t^{21}+\frac{6224480018922344450230333665132428495153313963178316990246561274639093714706604582918361763735549269254231573668095}{11485131144831087980380051383034231416060272550627223631828496586987357422469551921960211305534080896437959813458}\cdot t^{19}-\frac{2369146726849474702803405277741592563776341750046782855729884158356932084259087766677429093649928407147314508555315}{11182890851546059349317418451901751641953423272979138799411957203119269069246668976645468902756868241268539818367}\cdot t^{17}+\frac{2766573213948201864087413161462863956844654148285882095614268133516828426537331777643223379364060868544236940520329}{44731563406184237397269673807607006567813693091916555197647828812477076276986675906581875611027472965074159273468}\cdot t^{15}-\frac{6518332485262945516121741659194086916046229308670047829485996797269550806689938084704299360537112633542977062993355}{492047197468026611369966411883677072245950624011082107174126116937247839046853434972400631721302202615815752008148}\cdot t^{13}+\frac{994879105937362987870406108458658871779934011048080045134338661582265536874832679548507104053260758164151139885}{491555641826200410959007404479197874371579044966115991182943173763484354692161273698701929791510691923891860148}\cdot t^{11}-\frac{1193488153445042585657672969718433706870767326098852766774754802785489291730137063120317178642154795425666104845}{5648252563625585854227085081657198216835691290271030917554950807961546641651438031745461797038302101540568732644}\cdot t^9+\frac{9857085489709486693200773972475272947017406994029316509583218390915536595823109776751238193243067316324768710195}{698500567035030783972749521764940179482013822896850823470962249917911268017561169925855442233736693223850333270308}\cdot t^7-\frac{270189671234548231377320711425164229187800176999230658546254647113450988170561127072081102441622371148245681953}{498928976453593417123392515546385842487152730640607731050687321369936620012543692804182458738383352302750238050220}\cdot t^5+\frac{1960123576426401638946220490579720109073507901432202151665792626523452284384278868916889983772902842723666843}{199571590581437366849357006218554336994861092256243092420274928547974648005017477121672983495353340921100095220088}\cdot t^3-\frac{5981745265802651745098832086473035129998552102748385110370920359195418822478300137181640747121559664591583}{111954794716416083842322223000652432948336710290087588430885935526912607417448828629231185863246996126470785123464}\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.