Rule: Q[1, 8, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-\frac{36}{17}\cdot t^7+\frac{126}{85}\cdot t^5-\frac{84}{221}\cdot t^3+\frac{63}{2431}\cdot t$
• $P_3$:
  $t^{57}-\frac{7799784237853161230267262437743721973810611051091947936741064876}{548690853501721501530898924189894305034643899744150845899494709}\cdot t^{55}+\frac{905603959903232242912524960502355335870901399913155800037597526435055754}{9461152719510685708035591360156683331125976935807386854477372696992105}\cdot t^{53}-\frac{10548543004836655265009119559454504695867805425113901897931873109238782759498372}{25975433951820355929754679474257051421989740535651271883391100624255975411715}\cdot t^{51}+\frac{2013298059640784366461849138198394695299491820081506699107242674894466217332915439}{1652750650463863823373606566548316311065817804670360338462825912268836082568925}\cdot t^{49}-\frac{26973122028209090671108468393121880973020660971259147035106379629587073566910467608}{9815315087448660665341214507460409112656183288960711397809843683065944898521575}\cdot t^{47}+\frac{13544659164025949448840329995361706989628946523595693479055608798538156042381454303372}{2797364799922868289622246134626216597107012237353802748375805449673794296078648875}\cdot t^{45}-\frac{897727967108312472557454550000834727545499150922056517100558648805183144334550552}{131424233024330199183568058944149241113789628252469003917115595474455921826575}\cdot t^{43}+\frac{10137858187303379527993144254418646773526913787472255373197915498437075287850738557}{1291804046556221226121412872060784004118468785018170940941404511614774060880725}\cdot t^{41}-\frac{17937403159378371833258417105211886663824716960787630491414886507787428212437371790708}{2414381763013577471620920657881605303697418159198961488619485032208012719786075025}\cdot t^{39}+\frac{551987168906918889080586586413903855003550216554118987950513059912397343365491165206}{94489974530895744503382859755150544949021763315478924655823300855644222501749225}\cdot t^{37}-\frac{30798967984923481815874415095952014188685535216564887648189409887381361394641204827028}{8031647835126138282787543079187796320666849881815708595744980572729758912648684125}\cdot t^{35}+\frac{544826407348922789762475615210795497260231866800198607296253380587790526165310576321}{258549490749374070124641011857499842772598011709387387245054966077531993438852275}\cdot t^{33}-\frac{105179856729828161231708027253715745391153134772946372576700235725725994516175564656}{108423979991672997149043004972499934065928198458775355941474663193803739184034825}\cdot t^{31}+\frac{28807695860492293881052469693513917055317655545033804902122178327353448304078352396936}{77089449774079500972969576535447453120874949104189278074388485530794458559848760575}\cdot t^{29}-\frac{10535488980936424324320356701790333775705339079080214597277557917510509698946223455056}{87722477329124949383034345712750550103064597256491247463959311121248866637069279275}\cdot t^{27}+\frac{18220976982175766739595145886723634405558046886834800968974248994736009909877804355461}{568571612318402449704852240730790602519863130366146974303439979489575987462486069375}\cdot t^{25}-\frac{3901928975084642579607246899448182839722664329344945817951795956301351604057985182388}{553409702656578384379389514311302853119333446889716388322014913369853961130153107525}\cdot t^{23}+\frac{692544327334202256196915638651855762638002721545645351357166835898539882909312142199398}{546517236359855544501209844905789353948665384869362647849277091266974870886986655185825}\cdot t^{21}-\frac{281373080743216778031903079686156446024014777729106706181191334054301854079170229284}{1530860606050015530815713851276720879408026288149475204059599695425699918450943011725}\cdot t^{19}+\frac{5351460032785678524896305108341452967978892966866795921142822349799364507618744243}{252666313619905475959875101667031601455693659209136684165176648759581539938505157275}\cdot t^{17}-\frac{7769526131260508452479904428381887921274416825949502743534253831379584699404831256}{4089285180544562034370742479437816047733768851906132394405780008328924439697724483375}\cdot t^{15}+\frac{2571103772973124735070842570436360783468322414158114584510733330843124433893248324}{19901187878650201900604280066597371432304341745943177652774796040534098939862259152425}\cdot t^{13}-\frac{12600729742176535489376534660823102163933621266557931750973009934566822035818348296}{1961032436350069894974929443485479446521681675119477736400347209840321595535657998019725}\cdot t^{11}+\frac{5174258587977804953241524062963143448978080648952046909358895580593011429870894295789}{23255883662675478884507688270294300756300622985241886475971717561496373801457368198515918775}\cdot t^9-\frac{18852769449283865400046001988458099130518387660319557162263183129458575315008270124}{3776596492229351271843128864406766789484716553158938829431304561268641899381965775827371425}\cdot t^7+\frac{8338089261299228168908043389255129653104770200529143249000488254603268418603629446}{128584118663999340922277958954801821641979635024221012525875369586051378955147882367455741375}\cdot t^5-\frac{92371733017303174737487190999859586651643478434464613433687487255386857042274772}{231451413595198813660100326118643278955563343043597822546575665254892482119266188261420334475}\cdot t^3+\frac{963982297833992155603337101854639201653534852589353754642752497590116319720361}{1311558010372793277407235181338978580748192277247054327763928769777724065342508400148048562025}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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