Rule: Q[4, 7, 52]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{11}-328\cdot t^9+2112\cdot t^7-5040\cdot t^5+4095\cdot t^3-\frac{1575}{2}\cdot t$
• $P_3$:
  $16\cdot t^{63}-\frac{234671598234143765633661789270223013302353924635939486545100389690767199270999544833856297210419221356}{16497646471044866892978592775626964551478161310849288120924829533477545433268323305220391248855399}\cdot t^{61}+\frac{4574667135287898190214941695862048755339967304762765718180526352181988199987801715260886377876746450060445}{775389384139108743969993860454467333919473581609916541683466988073444635363611195345358388696203753}\cdot t^{59}-\frac{536296205051839814721396949100727466692630301364785409426203490105792640467434527933319514882533078889574901}{353147640300980220025937797830747498616789948059961989281579024271073794324020940454321642376488838}\cdot t^{57}+\frac{4854884773237187882696127795885902349352258911715673381726188654988580920930022119413894532326338168163844905290}{17833955835199501111309858790452748680147892377028080458719740725689226613363057492943242940012686319}\cdot t^{55}-\frac{18053306741074739255031695565910896520222911412311985955590165221616488333553908888419515770324888881847348709293615}{499350763385586031116676046132676963044140986556786252844152740319298345174165609802410802320355216932}\cdot t^{53}+\frac{7379868445984555547756610904636527230611480649593084075347681621813056276317248419994478616295776764616427287953971525}{1997403053542344124466704184530707852176563946227145011376610961277193380696662439209643209281420867728}\cdot t^{51}-\frac{1190162027183663618838766206594063675304210595453796372684963030796342800487535116270621120497832712888544422271788523375}{3994806107084688248933408369061415704353127892454290022753221922554386761393324878419286418562841735456}\cdot t^{49}+\frac{117084461164805971766159624687674731845704643101895350449307425810521177952604717361742915868641353761653292449382115325}{6071133901344511016616122141430722954943963362392538028500337268319736719442742976321103979578786832}\cdot t^{47}-\frac{1071031886163076370654113792919518202907950968013861010647488468979733837375698774139936527320104750876406060289873118375}{1055849374146871481150629937640125731294602323894354439739189090142562907729172691534105039926745536}\cdot t^{45}+\frac{184657442462855434676963858419712603769063651260725821597003076577408859902255521772439087027087951944412017748811554786375}{4223397496587485924602519750560502925178409295577417758956756360570251630916690766136420159706982144}\cdot t^{43}-\frac{13120040120656522259400624963525120473997285431557390253659589064422242992807884611374438440301850250059371583831805606686125}{8446794993174971849205039501121005850356818591154835517913512721140503261833381532272840319413964288}\cdot t^{41}+\frac{96386758896902156194808617869441129238079423590319078924769183714444670631021521654219909719032528538329290750511717272794375}{2111698748293742962301259875280251462589204647788708879478378180285125815458345383068210079853491072}\cdot t^{39}-\frac{18778179868026802511597923676537027121870049943036272850744631905100743949041080300729707142083023142519131213045921339064736125}{16893589986349943698410079002242011700713637182309671035827025442281006523666763064545680638827928576}\cdot t^{37}+\frac{1516338289580052273594195492251714062225207393187060183802734039449690290258140988601943363072736644155918984935592841259152409375}{67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304}\cdot t^{35}-\frac{50695803677344274507970732414815115488428324273925173295529533717301921966886206967869460013047319085405904130488917437999404048125}{135148719890799549587280632017936093605709097458477368286616203538248052189334104516365445110623428608}\cdot t^{33}+\frac{350028618836774656728541178178256275766633991653589450996174087758495981224695582351068520667610903513340898433942003730932442008125}{67574359945399774793640316008968046802854548729238684143308101769124026094667052258182722555311714304}\cdot t^{31}-\frac{15911988731236101878439240350261709550252957996177656666886458615904159331678636164915386959925999407999075811078563040840737981690625}{270297439781599099174561264035872187211418194916954736573232407076496104378668209032730890221246857216}\cdot t^{29}+\frac{592300460375891718982852082248787020687580894377484465901076276020416139924067374362581524685382101442883113600235827355978580962755625}{1081189759126396396698245056143488748845672779667818946292929628305984417514672836130923560884987428864}\cdot t^{27}-\frac{8967959840084428790486347584160871246692619488195101394137552211334794647028072873633054345504825071365197886671201849996662859606471875}{2162379518252792793396490112286977497691345559335637892585859256611968835029345672261847121769974857728}\cdot t^{25}+\frac{13695593591010606476395072011680291835540722262311165723010533633552672716865293939573579827620438877114418182425083530327801681690234375}{540594879563198198349122528071744374422836389833909473146464814152992208757336418065461780442493714432}\cdot t^{23}-\frac{534662287879981179593999847236373894475537953477398898867767260507100496564189187725495150670483740972911498888235204512373724116094171875}{4324759036505585586792980224573954995382691118671275785171718513223937670058691344523694243539949715456}\cdot t^{21}+\frac{8234415687080176403258234748847438177711032005514337950246584000737268513917735759663690708297168934408726681016608233889354867814144140625}{17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824}\cdot t^{19}-\frac{46434654191827294809407220014255533187200153778962453229082453404441761871111699770213587492609023637292196092478010390477999101288484375}{32608927702209881898533309893111819003828019744929506391492693784911876871319067630715884965428461568}\cdot t^{17}+\frac{56152581006122021217435979201437889291309960204524069859684892642015248935526268609309652840098179602933093937024959008204790506585364140625}{17299036146022342347171920898295819981530764474685103140686874052895750680234765378094776974159798861824}\cdot t^{15}-\frac{380402275679775498306617296478544055651993414664021899564657847166221808531487969162292068244508173541615190509319061987028515819969328328125}{69196144584089369388687683593183279926123057898740412562747496211583002720939061512379107896639195447296}\cdot t^{13}+\frac{1850778233272863631662084339099328762996213262780884586456581426293256159339710054250371689472652772288889846366341738231900834368080040828125}{276784578336357477554750734372733119704492231594961650250989984846332010883756246049516431586556781789184}\cdot t^{11}-\frac{3083716811583990434953242603970440917079125755115167303884995092050052915035676362746098185532779703321796314778455317156028012292368764609375}{553569156672714955109501468745466239408984463189923300501979969692664021767512492099032863173113563578368}\cdot t^9+\frac{410229609701060994664964233293945964360239344361474346273271327931411151657299562717553442461476225994513636862248815155793117718507594953125}{138392289168178738777375367186366559852246115797480825125494992423166005441878123024758215793278390894592}\cdot t^7-\frac{998767035297252618256928099005450864397940237261339353779707537266480069324184565461056192757588275707244949341243084727500382102374507109375}{1107138313345429910219002937490932478817968926379846601003959939385328043535024984198065726346227127156736}\cdot t^5+\frac{570676999298825140041405168061796982172043357377171750171128328530162246614863611665301079320197274120118448517678998610128697063045161953125}{4428553253381719640876011749963729915271875705519386404015839757541312174140099936792262905384908508626944}\cdot t^3-\frac{48560977569682808836047547183542374777029412953274914215891947443935936781656424066790158221483019252767155733087933479024742062843668359375}{8857106506763439281752023499927459830543751411038772808031679515082624348280199873584525810769817017253888}\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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