Rule: Q[6, 8, 27]

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.

• $P_1$:
  $\frac{231}{16}\cdot t^6-\frac{315}{16}\cdot t^4+\frac{105}{16}\cdot t^2-\frac{5}{16}$
• $P_2$:
  $\frac{231}{16}\cdot t^{14}-\frac{3731}{80}\cdot t^{12}+\frac{1182181}{20400}\cdot t^{10}-\frac{200960617}{5814000}\cdot t^8+\frac{14859361517}{1482570000}\cdot t^6-\frac{123220867}{98838000}\cdot t^4+\frac{4422019}{98838000}\cdot t^2-\frac{22771}{889542000}$
• $P_3$:
  $\frac{231}{16}\cdot t^{41}-\frac{15066705271199837419359155216063026920047883178814983952403817420410238972115168762774382729835043942897474487578223427}{107480474670152017732030602149232186203177001481046769518602893293331892139213664460310294441959547781661725048001600}\cdot t^{39}+\frac{17224292295940152514297628020636044598044215461261103299557583970016993101306132649898106387038419376226252235032413107449}{27407521040888764521667803548054207481810135377666926227243737789799632495499484437379125082699684684323739887240408000}\cdot t^{37}-\frac{579565182072850484128266226904816807910901209381415939215241676766359522687702536436638336021775524080370540631948965473587501}{335879170356091809213038932481404312689583209053308180914872006613994496232346181780081177888484635806387432318131200040000}\cdot t^{35}+\frac{16954838346976075556714698575581558294807728015626222285076693169226114797455015899864531247748803341236323972706590890668684792311}{5224600494889008092308820594748244083886466816824208754130834062880684388894144857589162722055378509968356509708530816622200000}\cdot t^{33}-\frac{568955525718231732988680080199676560652239138002340191620015156860955226344252320682658695224455095370521728087012466722546931455037}{128438095499354782269258506287561000395542309246928465205716337379150157893647727749066916917194721703388764197001382575295750000}\cdot t^{31}+\frac{191564834950763600356038931995420943790519461439116792253968210232775159184926310143248106352325623947654063819240167293184364778583}{42220135198749841922420616253696522621372039371827696174889453463734480968500118118205387913956742428449593767180385275616250000}\cdot t^{29}-\frac{33190726319458237761246769922191113520202025829461559312342278654251695328870109306088264839226293361143829178719483161784754968235459453}{9334238590415608801418361944448495703746037324520526208825434819029737724920848614163438186957126399793778438017075478659618631250000}\cdot t^{27}+\frac{1579226921436518479718709250246679714269965696342893920163031447608191178469760734373559609123136205010639078898727984440876076689415073}{732910585617818172555812123045585588590429597332722798618885993197890517660451817112092183568485480280104084762822222768829314750000}\cdot t^{25}-\frac{25259215332653933323914200434921177160061927510857679590413006438055214699179817299063924865411674689060840546675201339792365881352840023}{24918959911005817866897612183549910012074606309312575153042123768728277600455361781811134241328506329523538881935955574140196701500000}\cdot t^{23}+\frac{193431194272779501090401866857622353156858423254090415845323999173545345503376771910389708292938119559620527558910799895682738523624046023}{523298158131122175204849855854548110253566732495564078213884599143293829609562597418033819067898632919994316520655067056944130731500000}\cdot t^{21}-\frac{2586523853012743900618806839846486755227324914723511332802627681711037714638361369999150662430766380925699079421689150606640468232772337}{24918959911005817866897612183549910012074606309312575153042123768728277600455361781811134241328506329523538881935955574140196701500000}\cdot t^{19}+\frac{6835777468303974393376265301266654579209418908300888177797751207457373256307853930351456432376228506225529811331798237694474806683691617}{308208188372966694669523098059696255412501709615181850577099951876376065058263685196085081405905209865159559855523661048576117097500000}\cdot t^{17}-\frac{828384352832749685947130584567353132181029988019958075501206197198990601012610428507572254213127683571149871207844933250550714043862833}{233875625294780609484520468527651864401251297296226227790858198776779484661858914060558679419775129838856371890367954560390112385750000}\cdot t^{15}+\frac{32129535459839301540652470237925106384147510155020444857525606913217968154877681903688172455154994375472012938495770697837525449838927}{77958541764926869828173489509217288133750432432075409263619399592259828220619638020186226473258376612952123963455984853463370795250000}\cdot t^{13}-\frac{2628819870329507148616099185218994963152829158225025971559262580171544582402251599733616026963825518890605872475607954707942212574177}{77958541764926869828173489509217288133750432432075409263619399592259828220619638020186226473258376612952123963455984853463370795250000}\cdot t^{11}+\frac{323536306682699000072976522825864849899791196273269027808748617225043631941639721991470379957436212116775836064511525485179354190827}{175406718971085457113390351395738898300938472972169670843143649082584613496394185545419009564831347379142278917775965920292584289312500}\cdot t^9-\frac{97416965615696230226897167490579813640400409227123491213347525644863542979831733424962422416869072260443922134960554503733698494947}{1559170835298537396563469790184345762675008648641508185272387991845196564412392760403724529465167532259042479269119697069267415905000000}\cdot t^7+\frac{357716470428170922354169454262714685634666212812216470292390445677787083639101861535093581441795206116760408586298044999457435131}{311834167059707479312693958036869152535001729728301637054477598369039312882478552080744905893033506451808495853823939413853483181000000}\cdot t^5-\frac{7871218458313793899519415374514451461398264276526622674205887814307306904536384596510031099353995806524952157609365215447711851}{935502501179122437938081874110607457605005189184904911163432795107117938647435656242234717679100519355425487561471818241560449543000000}\cdot t^3+\frac{1408604468164116557613084483749454877809852974098074568744137784453149575307917130526916471378915193578816290218323060099737}{311834167059707479312693958036869152535001729728301637054477598369039312882478552080744905893033506451808495853823939413853483181000000}\cdot t$

Warning: This rule has negative weights!

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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