Rule: Q[6, 8, 25]

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^{39}-\frac{352510894625716943282019567406875941364066438499931839512337949556060568254471874387318080777520906308757}{2517922225887593349272077271280245468432084428018317944314011091577171950624307487189600411454260020080}\cdot t^{37}+\frac{1443542318383381678145159304717454311245423008088162955181885724328772477745483419589180801236311812005789789}{2303898836687147914583950703221424603615357251636760919047320148793112334821241350778484376480647918373200}\cdot t^{35}-\frac{46348495065123056186364433133007552590509429522113205122705401938549042250591287110998281067121705117559986021999479}{27001821080409391352059204359043773532725185833831677993085139746463460185283363799398129708993900038969414526000}\cdot t^{33}+\frac{325946143565646604687935799292666093978611234706950074539204088037224772513039708038311984453201013931457149977316403}{101256829051535217570222016346414150747719446876868792474069274049237975694812614247742986408727125146135304472500}\cdot t^{31}-\frac{4186864364165923223730039324795605563752343268860541492004896261347518585861714570685461385830035352887059986421621091}{956314496597832610385430154382800312617350331614871928921765366020580881562119134562017093860200626380166764462500}\cdot t^{29}+\frac{193438701613666448578183935676051974292279228022340501503806632735445319550767763302783223004672509556810171895567340534679}{43335391413330784739615767445856596166255230277127921459089797561222622647987428582677804608274991384417256931618187500}\cdot t^{27}-\frac{307448270709593631486029246847539434648028260644116854029952266107630537371631450847216374922916782395407567154340207620801}{88404198483194800868816165589547456179160669765340959776543187024894150201894354308662721400880982424211204140501102500}\cdot t^{25}+\frac{6040453822618156541238405694010724944824987874525686083034267800275347086748716689582151328902455350503738081485770776693499}{2887870483784363495047994742591883568519248545667804686033744109479875573261882240749648899095445425857566001923036015000}\cdot t^{23}-\frac{57428109353618607382661772975473297441750832299263857520713858542902268230374117037374800421120347202742077122235565581031}{58936132322129867245877443726364970786107113176893973184362124683262766801262902872441814267253988282807469427000735000}\cdot t^{21}+\frac{1302316077174676118425211138659505329459266498896119180577351909200070321982640604170699078678603869073206116698409505931907}{3712976336294181636490278954760993159524748130144320310614813855045554308479562880963834298837001261816870573901046305000}\cdot t^{19}-\frac{23775188475791925614955987908179832107417799142226918425754569175580403220791283086520132265016995988496486721683138076953}{245703266329100970097079093651466152446236025848269888206274231712771368520500467653808671668191834807826153705363175000}\cdot t^{17}+\frac{1067071429520139652175365018592761074496235316657939155260789701932789643392562246301576450076538915739170028451039872227809}{52917257000631610695084452093300766114788468319898267158213637915880577150829903660052334681102986163640817444790952507500}\cdot t^{15}-\frac{12016263449891131543950447179641622710829354595272368663930420826628950221887250677466126759033985802152572680951312375079}{3871994414680361758176911128778104837667448901455970767674168627991261742743651487320902537641681914412742739862752622500}\cdot t^{13}+\frac{18040630210422595868432727035894085296162134438069013801673913424862255260937464914080216113079121473976076289670556202163}{52917257000631610695084452093300766114788468319898267158213637915880577150829903660052334681102986163640817444790952507500}\cdot t^{11}-\frac{9400207084416357752408757743403100508315914711492648375724237420182848827859429362697574717525212054699464157294901701481}{370420799004421274865591164653105362803519278239287870107495465411164040055809325620366342767720903145485722113536667552500}\cdot t^9+\frac{86883462710198813190452116828695583379065015624972393790447110516785433381967282528353483721348254322429873306076613153}{73838033024137131202443421525535952718309490678927814639367866859368247187204516734956746066655329530661605736917608150000}\cdot t^7-\frac{150876001846969802988678639063402916520912820550142242492680598191358851926641927323405430201104077521833276606978529}{5162659219573815677569214838370806450223265201941294356898891503988348990324868649761203383522242552550323653150336830000}\cdot t^5+\frac{1366679230711048147713158607063430077371598622575916757240109597046923011818750940841369836791605155882138344021361}{4922535534942475413496228101702396847887299378595187642624524457291216479146967782330449737777021968710773715794507210000}\cdot t^3-\frac{867562412155253821605607925802061825604038911614479212358073198012065757110452885916390181318982060969218333579981}{5715063756068213955069120826076482740397154578549012853087072894915102332289629595285652145559122505673208284037422870810000}\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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