Rule: Q[1, 2, 18, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^{21}-\frac{492974097}{95285320}\cdot t^{19}+\frac{1092720951}{95285320}\cdot t^{17}-\frac{62676676797}{4406946050}\cdot t^{15}+\frac{104814789093}{9695281310}\cdot t^{13}-\frac{239868945099}{46239033940}\cdot t^{11}+\frac{190151996979}{121902907660}\cdot t^9-\frac{17182210131}{60951453830}\cdot t^7+\frac{42668603943}{1523786345750}\cdot t^5-\frac{107290416779}{84113006285400}\cdot t^3+\frac{479989951}{28037668761800}\cdot t$
• $P_4$:
  $t^{43}-\frac{88186444764315217611843095555521587690799414053147879926410892410827896054407913547944858522059749780552782483}{8129593605284088567884799856518750526623724600943891295414455184024596607033838892923784410690794859007026680}\cdot t^{41}+\frac{8012264149779481236318049782373213159109936363964618512260306206509746539568623881306840719228975038012478824521}{146332684895113594221926397417337509479227042816990043317460193312442738926609100072628119392434307462126480240}\cdot t^{39}-\frac{1638479810486437760498107329226996319982472287865658552941291157541814339008261387213423326857624870028020445441}{9596436265719962754716903056436525790023751478604451617770342347678804218866601741735626404679314739628996400}\cdot t^{37}+\frac{867996566660490583575845876696447463343943066324233895236633559381262670835637739741794459491396748725930559726633467}{2356913017443335378935235286402247263254458027710420016925107890517370991549849724515941444537296728304411774234800}\cdot t^{35}-\frac{3756941176802135826528008773478659716728222357477828553864269087375545687785015287309834629667060726247900952933813680251}{6444271572293567593084720320081024467190339139365830410276629994252595765095599116771487097653876714529922673112790160}\cdot t^{33}+\frac{151914677784456496098243684931116622638883338679496865684991855224783214660616518555488852911320016300994157031556556546963}{216615401259595147049370485304541708794875263343683254018162176397717934922190706675114304941592810472494446216677651060}\cdot t^{31}-\frac{307795225452439297277127615199942551311993912944050911764792478382922986446278298847679174575046610709402184607842139859784097}{469964582016664219519339055810566506723126631829229181145146241870365004808444527704779445401829279159630934490164154107820}\cdot t^{29}+\frac{33318685285176206700201806009128596640655497570725186906356091905229715355317819067171377536472623655378675771690035852390571553}{69279261659353087532592222882419717801426425898963956875706902896407255019175874342687314796304143738186973963636267545204500}\cdot t^{27}-\frac{1931833409951959689969177808013171404429517591432333701013128395956437968418468816614016223360718719814636083565671139737845774656911}{6909878918273047273956982014181101443655371005949715576804568641436211411985092119002461434125977144374899689646099506824924227750}\cdot t^{25}+\frac{11031948203331092399844940285494290007042384222080530865837767925317611456286978657710056864657811958546750212624064552385949817198324219}{85581890749535730628757763317719181064306978271929845293578376634389710270456639334377845944681242363026657612130386675809689527343960}\cdot t^{23}-\frac{453804740241924698961932761216667816560801109190611761445676069564725453303467840695264454458966687785861806365471661963140297206955163}{9649247814796585693588752975395014519409703519237484399349662214489038814576172305202513212628025115359674734455378895651350403598840}\cdot t^{21}+\frac{365680012087117870586125462655994560267105292704574942799114729605288334158405250500563413696136216720560352266635459959258896891975639}{27109791479666597901035067883252659840246309887381503788649050983564442383809246000330870454526356276486705206327016897306174943444360}\cdot t^{19}-\frac{420759514422391430296571837823320681353174235599795397612006945905541638137056108308801362587552553565989587091756597324206181965597}{139885404951840030449097357498723734985791072690307037093132358016328392073319122808724821746782024130478355037807104733261996612200}\cdot t^{17}+\frac{1399294096324799470310836557644350347217319657030480017739059706585826754656423597487240925098520368864503936035879706270925656995809}{2727765396560880593757398471225112832222925917460987223316080981318403645429722894770134024062249470544327923237238542298608933937900}\cdot t^{15}-\frac{6308164446426024289129195136421625030497533582231975208047988823145360401473041021457518913164396081652940835971613028817792043531}{96497220026099817614885804240645017185113502686364345926957406292619755209899801666357631272780142069668966949809307841419716307060}\cdot t^{13}+\frac{240093880966180187919444829822334962377523078641911908410762488225583944029231476256174594177848904501085373376842337193523844461509}{39853351870779224674947837151386392097451876609468474867833408798851958901688618088205701715658198674773283350271244138506342834815780}\cdot t^{11}-\frac{8329672436450669111527808781280720208195208531618492550916744901571608878124415731309168913321065895702071909758453985667631243563}{21738191929515940731789729355301668416791932696073713564272768435737432128193791684475837299449926549876336372875224075548914273535880}\cdot t^9+\frac{221721652019643817699415474866257500798028284676440849186995745581351547821795414284439533956262952377541370624516259750010322113}{14127546117714762320450348218330224757244232989062581142399493113372335345367034428066057783709595870988813994950355269224661267916400}\cdot t^7-\frac{16993699496896892386539037154573750890468337544403823501118881112510742009351802340405909532129235092413286421839444916350792363}{45842445565645861407175619728867464008200674393080620441663661327065333059456295389030677298159709050759620922389928322586145746912400}\cdot t^5+\frac{29731237943723201170363927581221467729466965216672635474582269668469866125233819191731458813886057645472702316712362070193492051}{7178926975580141896363702049540644863684225609956425161164529363818431157110855857922204064891810437348956636446262775316990423966481840}\cdot t^3-\frac{232019873271156359790595157336686293162060178708399486327569234244649345848079926911391178311675499171024198664550178091449981}{16750829609686997758181971448928171348596526423231658709383901848909672699925330335151809484747557687147565485041279809072977655921790960}\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.