Rule: Q[2, 16, 19]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{18}-\frac{318937}{47234}\cdot t^{16}+\frac{9281490}{732127}\cdot t^{14}-\frac{272844390}{21231683}\cdot t^{12}+\frac{132075125}{17371377}\cdot t^{10}-\frac{25545611}{9650765}\cdot t^8+\frac{115155586}{221967595}\cdot t^6-\frac{6801938}{133180557}\cdot t^4+\frac{3276767}{1686953722}\cdot t^2-\frac{20605}{1686953722}$
• $P_3$:
  $\frac{3}{2}\cdot t^{37}-\frac{816042248369903009826642602752908310324753276913166551160663917653}{57246075856848830718077886759360433931771385201514100736525804086}\cdot t^{35}+\frac{773376228164622743201427779484048485626874060725094727461548099335}{12409988472463732533289611814966247915279111477251308551274824662}\cdot t^{33}-\frac{414280064880126021687174140314470492761123039035806907036356634202704215}{2493675493645334878971747887711132822344099939350355191601714542406942}\cdot t^{31}+\frac{4697881115322757449312125545509852388256257574324887817586848168275827250}{15565361549044267712291394073293683907212365750461088050804250450185267}\cdot t^{29}-\frac{1533363738576901372834897919431470598472704762451909413323921564357461682}{3876431037118304219536170937793446183788520206053527675487648579548055}\cdot t^{27}+\frac{66346569715206817648041843836995440541489116890253745970445326059654357677054}{171807299996120361314062632133943328311691004052498400105288072694149345655}\cdot t^{25}-\frac{893970173935097233052953243339065514800131553629923826517052218070623774686570}{3126892859929390575915939904837768575272776273755470881916242923033518090921}\cdot t^{23}+\frac{17980652785898574950595469582734734273037883354089330184532496557596455524666595}{111072672459230960892318387054454648956428618072096509153285672526886273055759}\cdot t^{21}-\frac{31461516207833819186521866184039509260780855991443012432395038042140415349868693325}{448241703471545059178157445128755625481450290274093469581595280458858618221733713}\cdot t^{19}+\frac{1093735829086554443237757699777849358752026107910184858096232750144370294611422089}{47183337207531058860858678434605855313836872660430891534904766364090380865445654}\cdot t^{17}-\frac{1903136946359434754933801758263838428952388811968430667185563846443269487903285041}{330283360452717412026010749042240987196858108623016240744333364548632666058119578}\cdot t^{15}+\frac{21101313800390784413709528338208307877704557719094884458435434042193581092119920}{19962181126263140287286363953102477248161753817874607957075093461730545750765469}\cdot t^{13}-\frac{23445959997278345683117398254983314453635129039593205977058260081710951733391140}{168771167703861095156148349785320944007185736823848958182543971994630977711017147}\cdot t^{11}+\frac{142918102124308228016020908304983045262657543475683947700733257430717190447713175}{11420182347961267438899371668806717211152901525080446170352142104970029491778826947}\cdot t^9-\frac{48830038534891149641914237364596297525973523827962635494701935821453284337241}{67575043479060754076327643010690634385520127367339918167764154467278281016442763}\cdot t^7+\frac{78310293416620794324321999459995537511818666294786639270931510698990721253355}{3262909242274647839685534762516204917472257578594413191529183458562865569079664842}\cdot t^5-\frac{28277417346282848668546707082980020379121307210325146271623176791295127978865}{75046912572316900312767299537872713101861924307671503405171219546945908088832291366}\cdot t^3+\frac{465750248509168403247825198647151925949889427463535816458915552346906642225}{262664194003109151094685548382554495856516735076850261918099268414310678310913019781}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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