Rule: Q[1, 4, 44]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^5-\frac{10}{9}\cdot t^3+\frac{5}{21}\cdot t$
• $P_3$:
  $t^{49}-\frac{353916837235131723751618325714396}{29381880970450890571028887803177}\cdot t^{47}+\frac{46419706019288419119013940352401812246}{681806547919312915700725341472722285}\cdot t^{45}-\frac{10439103870567840274374649549967014912}{43498769007038601790225487735535687}\cdot t^{43}+\frac{26859203794545804616461361300622764256}{45418575304677936131722083013062233}\cdot t^{41}-\frac{578579494789127500870852688639622101708}{534541693970440325242575284692193973}\cdot t^{39}+\frac{22569734858020160954054740330728308149034}{14788986866515515665044582876484033253}\cdot t^{37}-\frac{1129167092807931746318619708705012759669848}{665504408993198204927006229441781496385}\cdot t^{35}+\frac{2802312473010218149170546244309758707558033}{1855582881545740877267064427972967231097}\cdot t^{33}-\frac{4704528488388425382449073329361517148360024}{4329693390273395380289816998603590205893}\cdot t^{31}+\frac{1331209612664338250377359597716769364968956}{2095012930777449377559588870292059777045}\cdot t^{29}-\frac{684065373117571774446656796558262166589344}{2260137102661386274313054002925916705285}\cdot t^{27}+\frac{268202104697763096149830815165588401327848}{2285893650839863610772462025751283277425}\cdot t^{25}-\frac{374689315404265518090103029232828061976}{10159527337066060492322053447783481233}\cdot t^{23}+\frac{33300818644655899710127269637547871428092}{3565994095310187232805040760172001912783}\cdot t^{21}-\frac{1952705043908763871147303096468592534064176}{1035326952338391026591063500703271222011331}\cdot t^{19}+\frac{2172076721366148338272635482640857917566431}{7247288666368737186137444504922898554079317}\cdot t^{17}-\frac{14347635786079151128212988220622036723953396}{390074654689846736783280101294379539822504415}\cdot t^{15}+\frac{855609862284438131361309278448592102466}{251647308804340467664026307761941860472667}\cdot t^{13}-\frac{196718932538843550555371014689332828524384}{859878854184431378007977893622555337235103139}\cdot t^{11}+\frac{4912040298224257530719779011492921400}{459910244705525786062387891044333394848513}\cdot t^9-\frac{59015915020800205921915988042615391700}{183026422778212301343063567718857160134379383}\cdot t^7+\frac{2424393201368486899526121832900758250574}{430417137566762595325104490085512421582682182355}\cdot t^5-\frac{1771348395450027843028330714933386986152}{37962791533388460907674216025542195583592568483711}\cdot t^3+\frac{1467102465239690063736875506975806143}{12654263844462820302558072008514065194530856161237}\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.