Rule: Q[1, 2, 4, 48]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{55}-\frac{474839113644184188621825289487691535573429410480327645265728043132751947353964525513}{35296696756878098795825420638227434423521047925229355488666552898639306090889305105}\cdot t^{53}+\frac{30183139239392438277411077357007827756978203148660806287821806690016729049692496653758621}{352931670872024109859458380961636116800786958204368325531176862433494421602802161744895}\cdot t^{51}-\frac{785640628973824815213272155236095584714712005587063612427527772269844467929205320481090563}{2299403310226823746054047027477326215520278667089066363309182588581857595290983781065225}\cdot t^{49}+\frac{77920515124109603428071050082306280398132737383731875805869539982788570270893453382085578191194}{80964289956396690922309049884504133374684532146873115718479628126555787787790829915087637475}\cdot t^{47}-\frac{46899378883769158498295422361636520440102497366170915949060252844877340501332715084805317118814946}{23074822637573056912858079217083678011785091661858837979766694016068399519520386525799976680375}\cdot t^{45}+\frac{254121630764699922354949911607400877199372287323902350634914473431341783628830492742739057227402}{76057363292372649048229713527867519230764257471305048099177832482522103679439870526294447325}\cdot t^{43}-\frac{147245235493931456503763973436962472579156247488026983608361545284538231258744308622464677743082}{33606741919885589114334059465801927101965602138483625904287879469021394649054826511618476725}\cdot t^{41}+\frac{41812423358109263472591337855285985772159720051320597895493571531046778247772546797487649216040669}{8973000092609452293527193877369114536224815770975128116444863818228712371297638678602133285575}\cdot t^{39}-\frac{18556954954629221293936783967473103929768174660977154176026329139814423247793830095860780648141129}{4565210573432879237057695130591303886851222058917170445208790363660222083642658275078278338275}\cdot t^{37}+\frac{22293395585031116478830334587560846636639453726402469735700053569003046513268760622491957298572477}{7608684289054798728429491884318839811418703431528617408681317272767036806071097125130463897125}\cdot t^{35}-\frac{1992560228187609819174418801553014695637095769419996758747521890284360473544816779039534368715607099}{1136737432784786930027366087517234667825954292670375440856988800551395298827021910494491306230475}\cdot t^{33}+\frac{270354652116792123031213932990553480494408148813857071553114392038642328445988587103859432979648764}{310019299850396435462008932959245818497987534364647847506451491059471445134642339225770356244675}\cdot t^{31}-\frac{324270664987336632508719089511904467373661363378625936181912205682998748063300135949100627980900492}{899021484660715803392054825611517073219414351600263557785671898990035659027822667810437506929775}\cdot t^{29}+\frac{333735270145677557600671125381742154242851728534958515192653048399375774415417998960395816454780348}{2697064453982147410176164476834551219658243054800790673357015696970106977083468003431312520789325}\cdot t^{27}-\frac{962916420418087628622089111818845432023287758249301619053876986899197533939972893000176058375332924}{27470100920188538436979453004796355015037660743341386487895530246917756248072359294207812711743125}\cdot t^{25}+\frac{653296398193156247338795172166394661502435716070202813789063669378191595527243110972820340324581251}{80212694686950532235980002774005356643909969370556848544654948320999848244371289139086813118289925}\cdot t^{23}-\frac{2388441899390520165580053514675002667707330065768360692335760458415409174326092467684429237753178421}{1553209451665496669660340053714830996832074861448055340001045817488451606913734962420499199472341275}\cdot t^{21}+\frac{120645978546809248588458663014778862811270058034722215798124780572004985839718561841692921939856717}{517736483888498889886780017904943665610691620482685113333681939162817202304578320806833066490780425}\cdot t^{19}-\frac{35826517675922202968761448446332952430946062360086946442346902564610371290451134140648288045863901}{1284753497056645393422750414801156503552456984160737133087284811996620464978027684965104276106751425}\cdot t^{17}+\frac{1342434663622077048243162175836500681184704013657576966523045194626757986886777650015993478604039046}{520325166307941384336213917994468383938745078585098538900350348858631288316101212410867231823234327125}\cdot t^{15}-\frac{2074935849144459860389404974476300542331603112919250321846315198642893240296127287349984317002286}{11562781473509808540804753733210408531972112857446634197785563307969584184802249164685938484960762825}\cdot t^{13}+\frac{940308487406916776714837785796576086963966720075845197768946004771087640811295935243838906101058}{104065033261588276867242783598893676787749015717019707780070069771726257663220242482173446364646865425}\cdot t^{11}-\frac{523312349806566287946233946585109459466220737595981068018782239622932776364345039845318174018806}{1674500989754647727772906608818561890130143252901135297915672940872322509671816629031336364231135925475}\cdot t^9+\frac{16310562012328497610288323206446139576819423207065928987669965787140916835859780104411788045830483}{2372023679820222653486309595091982837474355147915174879236323813686804408422887800391167478620305768208975}\cdot t^7-\frac{53247726615340387266997725770438813149535908913467009630186914986355026618282873959224810480541}{624216757847427014075344630287363904598514512609256547167453635180738002216549421155570389110606781107625}\cdot t^5+\frac{37679601440216012641908220469817910998283880247038840872741718742364017354487271405562729030641}{78276781434067347565048216638035433636653719881200771014798685851664545477955297412908526794470090350896175}\cdot t^3-\frac{250529212125800956619989303817271189760375193968256532155817725397359473132090875909223501}{330281778202815812510751968936858369774910210469201565463285594310820866995591972206365091959789410763275}\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.