Rule: Q[8, 43]

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.

• $P_1$:
  $\frac{6435}{128}\cdot t^8-\frac{3003}{32}\cdot t^6+\frac{3465}{64}\cdot t^4-\frac{315}{32}\cdot t^2+\frac{35}{128}$
• $P_2$:
  $\frac{6435}{128}\cdot t^{51}-\frac{116708586018140419033359774673269474181701028856150787126411}{182624663041891523938538958126450436698777855518633956160}\cdot t^{49}+\frac{258311498564574912417175911936724020807840928109237613333235029}{67571125325499863857259414506786661578547806541894563779200}\cdot t^{47}-\frac{911914347933291720472631719259761808504636360560204514624467313961}{63746599632076571562938531645702536533202000691623331469297280}\cdot t^{45}+\frac{31118538383122838760718651702569780388069846646639180702725561910031}{828705795216995430318200911394132974931626008991103309100864640}\cdot t^{43}-\frac{60899915673974960372043780744500326741972180525967523681038402458821}{828705795216995430318200911394132974931626008991103309100864640}\cdot t^{41}+\frac{221908296020816072119467489938782520853587054001828886625782867931949633}{1994694849087308000775909593725678070660423803641585665005781188480}\cdot t^{39}-\frac{16160657677456790597470290166358200506617884684311001463857244550380221}{121135314721901295593678720266741583238487275524792651720998857600}\cdot t^{37}+\frac{554965015294675433579287929300098126301661214164574374660391253505341}{4310671109473064122477756261744407691820042687593972741422932320}\cdot t^{35}-\frac{1741647941698893181844934078840315211544439305039432234264223318819963}{17242684437892256489911025046977630767280170750375890965691729280}\cdot t^{33}+\frac{11564748817833536261852537727505891124648306781262157150066794532885}{178372597633368170585286466003216870006346593969405768610604096}\cdot t^{31}-\frac{3466648374397098240616329005389526574061738468473860838237672453442193}{101509351932752800303508453905594116613826811675600003265765825600}\cdot t^{29}+\frac{55046517893684659826476350014605489468625614288118325923447041866000227}{3727843441668335597352982876188197730818122566707379430277262216000}\cdot t^{27}-\frac{259914137720711548426786717162074546862598978765633028094777328366991}{49704579222244474631373105015842636410908300889431725737030162880}\cdot t^{25}+\frac{5026552725702142010233509769050810880831907732559655437025907260217163}{3330206807890379800301998036061456639530856159591925624381020912960}\cdot t^{23}-\frac{1173718537803956561084294413198351720971005591249287433639033160436983}{3330206807890379800301998036061456639530856159591925624381020912960}\cdot t^{21}+\frac{438717673865888122665179578310528529801181803866480780552634233246407}{6660413615780759600603996072122913279061712319183851248762041825920}\cdot t^{19}-\frac{16029850364415438867940136605611186403647679914682036323095748680849259}{1650533749160669488524677776622959446967480584097748137583843489985800}\cdot t^{17}+\frac{5852988799384759042240786115381751807507657723153317375534545357961361}{5281707997314142363278968885193470230295937869112794040268299167954560}\cdot t^{15}-\frac{503734868892524773650271058984707987869106607413716460372475998170317}{5281707997314142363278968885193470230295937869112794040268299167954560}\cdot t^{13}+\frac{756687403772240007215908267991511834829981861091788898381447817621}{126547858699834432411475925370335352302172534064493173726478794692480}\cdot t^{11}-\frac{1255884120611918647251658016575658381075995913721325931118240884992177}{4827724880683463695838359667323071489116500871039975881760930130241296512}\cdot t^9+\frac{882847552278799841373418891371784416546637063112188245496451315121003}{120693122017086592395958991683076787227912521775999397044023253256032412800}\cdot t^7-\frac{2869147727646359174310550111493052870492795049964220661771706274459}{24138624403417318479191798336615357445582504355199879408804650651206482560}\cdot t^5+\frac{151117748058554155592875447596289004286773401819150531023684663}{165333043859022729309532865319283270175222632569862187731538703090455360}\cdot t^3-\frac{50739790649386497387455745440598025210527384685096486555011733}{24138624403417318479191798336615357445582504355199879408804650651206482560}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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