Rule: Q[3, 10, 26]

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^{39}-\frac{3189268649727806706148217532503789540996578918504609895242606216498470312696897712229}{130683639487006596138008922526980487256268256278467240700625746330984487530630113336}\cdot t^{37}+\frac{1810268022144681479045974479080611279650410921731492041833578734650546744384447367747985}{16466138575362831113389124238399541394289800291086872328278844037704045428859394280336}\cdot t^{35}-\frac{12686477701187916753513766574344579586986843120957651435028266818121414351197903736417608598255}{41851770357198228124096663018125015167828259632451719267446070265659882113941347270204366832}\cdot t^{33}+\frac{50178880460993168331676525028847129690176177908779795802474879389497108881907976942806820785}{87711510765654143908841400897604997687619612045845816879060746862529590960590348427893494}\cdot t^{31}-\frac{2803823811706129806616380401522780584040361462660187545791805708406782708289544419430899428230}{3580908053694910647714693967205871947190738541698525357525185482902916483928413944773074539}\cdot t^{29}+\frac{1625392153533765844526715361480222701343445380848631767626886196089167348461553277119290399300579}{2023368741992132990334789686861196166334384264691914588973796110252447940223202940272646813428}\cdot t^{27}-\frac{57534418523565508818046467658001933901792280080145747891097681030182493963100633166878214664361455}{91351351721792967230300319566066597287467200691090514220705831792508668116003125340457646872916}\cdot t^{25}+\frac{12871052061373662114264982019592323176641981143752872850362991980682762656285003774399741751702525}{33760282158053922672067509404850698997542226342359537864173894358101029521131589799734347757382}\cdot t^{23}-\frac{1774914873048668677613778646382805847355263972937617267905900162443757469318963606647723816076135475}{9925522954467853265587847765026105505277414544653704132067124941281702679212687401121898240670308}\cdot t^{21}+\frac{3226805290672657240588117340874049078449167491369112584607504139807730923914604487497023271451325}{49751994759237359727257382280832609049009596715056161062993107475096254031141290231187459852984}\cdot t^{19}-\frac{14072216523408247780821087116051051653418693809807768630360065804193466754175806303865862050690465}{779447917894718635727032322399710875101150348535879856653558683776507979821213546955270204363416}\cdot t^{17}+\frac{5628048928691849322625633859520723955782432142226912071001963770896197283570529925503628364619975}{1478658550123804470717458376317098571883064631781301492769251032458375432307890405253380240630598}\cdot t^{15}-\frac{18052162272965958002698744569536742510804966175762760953682878660390358624446430877965706282769525}{30312500277537991649707896714500520723602824951516680601769646165396696362311753307694294932927259}\cdot t^{13}+\frac{8141801203668925503660571057833352841355667452775410302746748095419048079908705129005432518866725}{121250001110151966598831586858002082894411299806066722407078584661586785449247013230777179731709036}\cdot t^{11}-\frac{5704699813997511463527627703720864614681536199862084113871198033288015987971557691151125410466625}{1091250009991367699389484281722018746049701698254600501663707261954281069043223119076994617585381324}\cdot t^9+\frac{3289400965953311703505810426923253849160034835050204441151529146517427710399497779872257965190}{12481617761339173032232663353029626180307045568271574365434560185751580855069545479638827325322989}\cdot t^7-\frac{99034931604417324901309289863178690954412830815451760515861968637253304852743594903647500375}{12763158011594943852508588090316008725727505242743865516534587859114398468341790866397597866495688}\cdot t^5+\frac{712160582984625361289436190251915662357262679474503571826066525762926621961047806252796545425}{6443571487568075939252192901596682119531571932550974390776176213444326312445698417407015837170823056}\cdot t^3-\frac{7342950638357166201696245276812419368672700060106002045029861166273625656139670881159656325}{15035000137658843858255116770392258278907001175952273578477744498036761395706629640616370286731920464}\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.