Rule: Q[3, 10, 28]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{13}-\frac{124943}{17112}\cdot t^{11}+\frac{2882165}{359352}\cdot t^9-\frac{1552265}{379316}\cdot t^7+\frac{52195}{54188}\cdot t^5-\frac{488345}{5527176}\cdot t^3+\frac{3421}{1842392}\cdot t$
• $P_3$:
  $\frac{5}{2}\cdot t^{41}-\frac{3456646554674717718481692338548395717412232611661359053764791118911771492181232687616018083462907}{141624458707824340765189198664491549792777935838189778076202864950612767001396388892389059616888}\cdot t^{39}+\frac{2507272945689870343794200990017314303457056497298022482855004434792939237924424839697095334819246035}{22801537851959718863195460984983139516637247669948554270268661257048655487224818611674638598318968}\cdot t^{37}-\frac{4168954584765809634200978775452733472837192058289966520349919446764307128144800458781526572832399971047}{13749327324731710474506862973944833128532260344978978224972002738000339258796565622839807074786337704}\cdot t^{35}+\frac{192214949368231072951292969637706330941124290214365656563229038577694700619535489439694752200091286760335}{335876424647017498734381938363509494997002359855915039495744638314008287607744674500801001398351963912}\cdot t^{33}-\frac{3864057996134153055617968507212794917993978494737014645923995441758273749389527756732122467645887178926925}{4933157329194715838624777672452981518910188481006293651566122914051364806560257832893681638127112128722}\cdot t^{31}+\frac{520619819193051449257774556234933934567384811056181443326357513553756546862024823516666914835145311575598621}{647834951198441554162628061437293153660754106650858756629860851067842133145380956055167030606950757291202}\cdot t^{29}-\frac{1011593897881415678553893780704966583413428200397455415707627704746836856741597106418771311138010092209066265}{1605504009491789938576947804431552598202738438221693440343568196124652243012465847614979162808530137634718}\cdot t^{27}+\frac{521646679859420079801992028648847428429512011591640144886104271350368050026451417385242166620545363946062827}{1367651563641154392121103685256507768839369780707368486218595130032111169973582018338685953503562709836982}\cdot t^{25}-\frac{148941811785070751024279799281269690522506951792314295536462815563466309816528438164096354389193978412174025}{832483560477224412595454417112656902771790301300137339437405731323893755636093402467026232567385997292076}\cdot t^{23}+\frac{2755393279349174534090047129219081971159577625189526400369514035454413148115108685076291305475276440883567075}{42456661584338445042368175272745502041361305366307004311307692297518581537440763525818337860936685861895876}\cdot t^{21}-\frac{1922925301745695318155427923710203536521301137878258333963431632896003489468496856297069035017873534215235}{106407673143705376046035526999362160504664925730092742634856371672978901096342765728868014689064375593724}\cdot t^{19}+\frac{80638106728312627491063133776937683153530360979999661959726753915985657640183973926691582351410474638675}{21150621689848396545867115516597553625879187467304093787858802058796652005693660085284415068914372234508}\cdot t^{17}-\frac{966743596131157895727044217859349354115050438896577833218383667900554568797424995372142067743774572875835}{1618022559273402335758834337019712852379757841248763174771198357497943878435564996524257752771949475939862}\cdot t^{15}+\frac{1745065698811882116398651870119157574413628085646525171654894687989792645324351379347198857228296490916157075}{25812313888088587462360684178475479134014276841441518927124927397164698692682568389551483929970909989668618486}\cdot t^{13}-\frac{58684968057257878989367440359930297284816563089454722392492735638550385983627298741054726328574254775107925}{11062420237752251769583150362203776771720404360617793825910683170213442296863957881236350255701818567000836494}\cdot t^{11}+\frac{20131595875164337091642640662481866204218971542563427793224904716162830590623714845028689752298013518767790}{73917080679526409551305595601997962974677247318673440564039564819153455347227354933715613072189424061323771119}\cdot t^9-\frac{550823575914166504027950032429506632129122266397163415490466655884944623534967623838815904787131262132475}{65704071715134586267827196090664855977490886505487502723590724283691960308646537718858322730835043610065574328}\cdot t^7+\frac{66391581247061359202598736811935672569439904501249282691149766548874919301177177654334778423771399895}{494015576805523205021257113463645533665345011319454907696170859275879400816891261044047539329586794060643416}\cdot t^5-\frac{399994688227496872019010830935190967104983832691190905243916747362805690372498996513549595822823325}{461621112752702011249371401105373695392207633528015241617733425880739767976439375073946061340761430515683192}\cdot t^3+\frac{349468800635350368266760191317685311699118176136383624034388417400493265226892167382792592369826025}{290975174738453167757520439830087219328888211667158940633044636113492967081148952754944000665126621701718972024}\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.