Rule: Q[1, 4, 46]

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^{51}-\frac{3074862911072572473401555995904660783}{235787960091625877486601228484816929}\cdot t^{49}+\frac{105071650121552508094151343376986197143552}{1312159997909898008212935836518006209885}\cdot t^{47}-\frac{37558284130813724741044953814587663897954664}{122030879805620514763803032796174577519305}\cdot t^{45}+\frac{90540687737470876752451048199844855022525874}{109039478648019571073186275816323433866087}\cdot t^{43}-\frac{23886693504179462855355744370370759309100890}{14292361707914200037575226137927519313817}\cdot t^{41}+\frac{314071342491193110776084974988887913236237215944}{120613240453087934117097333377970335489301663}\cdot t^{39}-\frac{90259835344736136192378837238386438943841056}{28063949102584562826817751728319218085835}\cdot t^{37}+\frac{72034331798041258627221884299113102043869689021}{22516641829973680908050109470021452644201615}\cdot t^{35}-\frac{944496568420984594940327602466095139529670850959}{364769597645573630710411773414347532836066163}\cdot t^{33}+\frac{63154004266902897913764999684012165760251610400}{36803062853129395691088799616517822597764019}\cdot t^{31}-\frac{6078107573265721245930239279231727385482404413168}{6507018951548458638156700345101102763172406069}\cdot t^{29}+\frac{1004356736832717635638989746071757205062185431812}{2404071041212484718530800620111244863241036725}\cdot t^{27}-\frac{995702071406304041523708994313902256955209686852}{6499895778093014238990683158078550926540580775}\cdot t^{25}+\frac{846046227941468078836455106798619759936691571984}{18459704009784160438733540168943084631375249401}\cdot t^{23}-\frac{615002029971336094682857828924423744784271177440}{55379112029352481316200620506829253894125748203}\cdot t^{21}+\frac{2666887395804492098101828336059577667529729462397}{1236800168655538749395147191319186670302141709867}\cdot t^{19}-\frac{8862356173238723991648021168111815039957254980833}{26797336987536672903561522478582377856546403713785}\cdot t^{17}+\frac{66359356167426094848966268975796869887028395922976}{1688232230214810392924375916150689804962423433968455}\cdot t^{15}-\frac{51656828438791050448905455588137289604195251048}{14638545279758839227915697353971866112680572774993}\cdot t^{13}+\frac{3086497123839030870996345216341866930279587487090}{13353731420973851877219404224673258479252224041433999}\cdot t^{11}-\frac{421543851344106833295219732281286187892433717778}{40061194262921555631658212674019775437756672124301997}\cdot t^9+\frac{6903035942861546616697777596982076860888782904}{22256219034956419795365673707788764132087040069056665}\cdot t^7-\frac{118632310585964593684332715964893745891777561152}{22412012568201114733933233423743285481011649349540061655}\cdot t^5+\frac{576043164025592741500255715966813912353124917}{13447207540920668840359940054245971288606989609724036993}\cdot t^3-\frac{22822382673439416583129201343282632832434433}{219637723168370924392545687552684197713914163625492604219}\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.