Rule: Q[6, 8, 26]

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^{40}-\frac{1188679641939255157663064435774016002609900591237855264493337500903767036061725563779091012539510957737593571111}{8498062580836962605514962553601883044646250258256244404582346687380663435423055272048289936880742088574445840}\cdot t^{38}+\frac{58284910561017626792621425631505145147774956133560881995926599097719574604950688408288069442585283509975199642075697}{93181256198877294969471564400244647584546134081779719896245431427128974569413801058009499157897337001218798635600}\cdot t^{36}-\frac{2773867391502034552932835647347026694547337567246578572354415603618541911991817804196193604423129433866584294408609727269}{1619956139017481773044263147098253198257334541011740430396226825360637222889258931393495142860045203766188814279906000}\cdot t^{34}+\frac{400830538120296902114609110723102804650379217212080460250294642524264184979919160040027442475369700061095479795986965194256817}{124907730571529818036686062621477749259880690618798378223470067011197783469140615691927563924688072964644342393061077071250}\cdot t^{32}-\frac{961485369844559161177744774857873295502903720667842839969047238593328246515501425098162389399582992810886864598848557215145849}{220425406890934973005916581096725439870377689327291255688476588843290206122012851221048642220037775819960604223048959537500}\cdot t^{30}+\frac{332101057507639557742801070392359926842042606411536365817011502238080515387639579440048158238817656949730502979686141066835903297}{74713327730748391158980737456920950020261968647910881789223762304846081593578553460171487310507865865889115912886533137062500}\cdot t^{28}-\frac{44413048000619054215752792749091337543602195810100385267148744268503182997219483224551743769065900968455406777531062808093598576857}{12829772637924113729820172236102465537479385256219256620845504462988169131249309200180647800960410726490478984560875470296372500}\cdot t^{26}+\frac{2723835132849780028081389449006635277979219717723204022296370954800451543939656851508052277760563897623173919269061123634359562168047}{1308636809068259600441657568082451484822897296134364175326241455224793251387429538418426075697961894102028856425209297970229995000}\cdot t^{24}-\frac{20723902985653052392101530056081925015162405108245056548824733792747175852650509136389406523247651203593735377452361157558803830329581}{21374401214781573473880406945346707585440655836861281530328610435338289772661349127500959236400044270333137988278418533513756585000}\cdot t^{22}+\frac{1065971816624394181393023995680946778075124307136991069146171186715896766944351158909832844803518478548037288724261688395111239111217}{3053485887825939067697200992192386797920093690980183075761230062191184253237335589642994176628577752904733998325488361930536655000}\cdot t^{20}-\frac{36694251934780532189490497262587828886855722101129089903346873041090076505738896709566458063551178447144299513341360646010695457361}{380628434770546421181091536422873700571756831285618388945305686422723798880000281257436947225168971968734154915919601902698475000}\cdot t^{18}+\frac{192388253796305681365636278583685536879813488978856602794618290932144035073741633040160791789516175432219516001428089741612559501761}{9552778605721707207145577717060083155722150695775464390268492191468085721041261960787138128430891081455831904978037119909620092500}\cdot t^{16}-\frac{1220797531342982892600533114645046724159802187569267836320878645973859116984627320469119117334904394400016151625789823487377845723287}{391663922834589995492968686399463409384608178526794040001008179850191514562691740392272663265666534339689108104099521916294423792500}\cdot t^{14}+\frac{9936512864466965767754644255001851018404081071356791198178418194568764059195514058927187723598170486931435411342001226918163904371}{28658335817165121621436733151180249467166452087326393170805476574404257163123785882361414385292673244367495714934111359728860277500}\cdot t^{12}-\frac{10392729094760187472773706680967368998353289170970742390525272833890578663114680607758706079383742717703065314522670257188775951797}{391663922834589995492968686399463409384608178526794040001008179850191514562691740392272663265666534339689108104099521916294423792500}\cdot t^{10}+\frac{71808933556781906531751539463705734303397606655159907678082598637533251432323976345503306148175351364731054892130974679633537027449}{54832949196842599369015616095924877313845144993751165600141145179026812038776843654918172857193314807556475134573933068281219330950000}\cdot t^8-\frac{177085592308900202843109770150114270281877816808934086512633865474794594451032745837442693156264709101342102225486517382662858873}{4699967074015079945915624236793560912615298142321528480012098158202298174752300884707271959187998412076269297249194262995533085510000}\cdot t^6+\frac{20295629118985905723246972325965948508836398919092858704167297624347432852078722658906287876776745183468409974084474148878297}{38211114422886828828582310868240332622888602783101857561073968765872342884165047843148552513723564325823327619912148479638480370000}\cdot t^4-\frac{4013564280159674239751042282008068393641921821091670285237595358459917694709444614872681197955349193310768347564983796815597}{1566655691338359981971874745597853637538432714107176160004032719400766058250766961569090653062666137358756432416398087665177695170000}\cdot t^2+\frac{1725339343189928990092671131629461451579444978522761937668694469087848631279552469299318900714723342592830391291305311}{1309588348796771501957913874029165579366491742442531155421327660180206921757607057658372991724210083860260794899156296190705813300}$

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.