Rule: Q[2, 4, 6, 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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^6-\frac{25}{14}\cdot t^4+\frac{45}{98}\cdot t^2-\frac{1}{98}$
• $P_3$:
  $\frac{3}{2}\cdot t^{12}-\frac{1595}{364}\cdot t^{10}+\frac{318813}{66248}\cdot t^8-\frac{10310751}{4183088}\cdot t^6+\frac{2471775}{4183088}\cdot t^4-\frac{33827}{597584}\cdot t^2+\frac{31245}{29281616}$
• $P_4$:
  $\frac{3}{2}\cdot t^{37}-\frac{4828174601638505601380657911260985138488479992175030278240075935507932870115830239179402103487459783}{349864304583975554096596587864900158201341059277209282391606660810476028682660902587011592846385084}\cdot t^{35}+\frac{219299194150099913919580575630158383451741529239002683981756886641292443318602333734152257561413676516547}{3756842902622729499889254160493297898766000294518673274321072323782891595994412771979330483984483031992}\cdot t^{33}-\frac{90211066336661793078535075738295580277282271638592081620000334417988406068377356174801087819881624264802020015}{599449367228287964461329172356631599322900538993988544997218942127445748840060490722565930685532081550707504}\cdot t^{31}+\frac{22631512631297165639892421798666446734469753491043354762161343592452451378482104324711382498169244112927501537}{85635623889755423494475596050947371331842934141998363571031277446777964120008641531795132955076011650101072}\cdot t^{29}-\frac{1518995513109624355160710986537454150635100589987695283558089707799508572590649391664388380452719492516340061113}{4538688066157037445207206590700210680587675509525913269264657704679232098360458001185142046619028617455356816}\cdot t^{27}+\frac{267603310322785462461277789371640806208743262755182747566570407342446413099382232721054061861150358689072807763}{847886781589776226027719912548391006263631688592753028324166823951065337056349296924696865851906445019132592}\cdot t^{25}-\frac{65627171964079792048955972652084233991622272851347978431194669281028024677959075125346368063569961535928537277565}{290825166085293245527507930004098115148425669187314288715189220615215410610327808845171024987203910641562479056}\cdot t^{23}+\frac{1686408959172178793407770683018665299910949810153355063839557403344364790719249013806229707756328991201483463318475}{13668782806008782539792872710192611411976006451803771569613893368915124298685407015723038174398583800153436515632}\cdot t^{21}-\frac{705921814192767205317831159429174646605736327438693512306026651557350468154356355767329222979231315036824138259855}{13668782806008782539792872710192611411976006451803771569613893368915124298685407015723038174398583800153436515632}\cdot t^{19}+\frac{11842995068518062137595771884197184483685874324460249064029809663952547482631243610150587050582153873129317250745}{719409621368883291568045932115400600630316129042303766821783861521848647299231948195949377599925463165970342928}\cdot t^{17}-\frac{978280226777457395863507979312365599079037512219766915229389467694449259139387566051497730876774132613262138065}{247863819127094243313360363165810290973470262947348356636076792625174744027466469546503567072243226805082218992}\cdot t^{15}+\frac{140205701972703098617714032087252448656141302728730142938341722939263291886316425997585788160782425748161412135}{201097060801227404952348973889242311544513609561056213874552869488349320626057701707540629888801108539972366352}\cdot t^{13}-\frac{133843322309733320592380643460706052903455577139109061163085150442786315910733487511999440147810714899203644825}{1522592031780721780353499373732834644551317329533711333621614583268930570454436884357093340586636964659790773808}\cdot t^{11}+\frac{562315014148613896273044365232599931087196961485308170092706725817983494314648814495341836392987103521583075185}{74607009557255367237321469312908897583014549147151855347459114580177597952267407333497573688745211268329747916592}\cdot t^9-\frac{30394359637459955778330717368892214936262807156030025866941823277053885200294255938925871858815965555832905345}{74607009557255367237321469312908897583014549147151855347459114580177597952267407333497573688745211268329747916592}\cdot t^7+\frac{11859104122726910252854779603562648837991727410806993615888475893622340992696953797589856243310723682538607405}{969891124244319774085179101067815668579189138912974119516968489542308773379476295335468457953687746488286722915696}\cdot t^5-\frac{155253209578345140113714927699880657395220315610176152597191268259141006159607859971669242590231112511814805}{969891124244319774085179101067815668579189138912974119516968489542308773379476295335468457953687746488286722915696}\cdot t^3+\frac{69532688652188178463405677948200426786268627063695201161719336085810920844939234848905483850617448897225}{138555874892045682012168443009687952654169876987567731359566927077472681911353756476495493993383963784040960416528}\cdot t$

Warning: This rule has negative weights!

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.