Rule: Q[4, 13, 18]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{17}-\frac{20554887}{1192364}\cdot t^{15}+\frac{16554685}{596182}\cdot t^{13}-\frac{43561973}{1850220}\cdot t^{11}+\frac{927511585}{82273116}\cdot t^9-\frac{83298215}{27424372}\cdot t^7+\frac{1686197513}{3907973010}\cdot t^5-\frac{14357343}{521063068}\cdot t^3+\frac{2723149}{5210630680}\cdot t$
• $P_3$:
  $\frac{35}{8}\cdot t^{35}-\frac{518314344812687970808252457270465158224519460506987694234652110304776671069}{14135785039874689002573043478302730158205509620767976562081970768437233368}\cdot t^{33}+\frac{2544154249594504128777776704250992819909273876975781179008553080865281191273135}{18150990526882731346985722964480628374506701876230662268284254192617427518756}\cdot t^{31}-\frac{9781183538488501840780826319639470180612098228043612126636193532082271640779715831}{30221399227259747692731228735860246243553658623924052676693283230708016818728740}\cdot t^{29}+\frac{73274742286838692013765341459082403680209975852653641240404996538109281178511159367}{145410088695757820507784969526794242270707603447984005177744923682464090118618972}\cdot t^{27}-\frac{135546194070265104779467017257236699856398260379549561202908170728845849225738624761}{242350147826263034179641615877990403784512672413306675296241539470773483531031620}\cdot t^{25}+\frac{789951122514721503818614112766433952553791039345530215786250222100047896422541216204533}{1731600618951297606960236786961546089236844299399345769779838390120111840683167507868}\cdot t^{23}-\frac{66041597257807635857159662508166851279774910194624923759133936211911176615776952001461959}{237681006696923762833629023323373956683509454487118895443258686852573612218989557493012}\cdot t^{21}+\frac{4616127826052313157210931717922904111578342294130891902578670884075911912116294632836877463}{36305773772955104772836833312645371883406069172907411278957764416730619266450654907057583}\cdot t^{19}-\frac{58202627033225695323502387639430337788914984064695730577739316569863284576894736528021880}{1333975799006294812904630419630465501177780098706627822563492833583945295788157131639653}\cdot t^{17}+\frac{22022015669660745041603365627195979580778063592594935790500627558410004241872955468475822267}{1979620085725341502350471542731610803747825666480635688684223365038574818949625183353245052}\cdot t^{15}-\frac{109199878980124890528395003701600292864852103045583996273690404323248655811648305794184277}{52725958699706432265993188789461788961806494748878916647763818439284075080982753067519844}\cdot t^{13}+\frac{196644314917637578382433255382421946409525217265509269465510770446644935892488100619218051}{717884206911387577775445724287287434326134582350120634358015066442560099179534407150077876}\cdot t^{11}-\frac{263962884722656316484150082422434897906876980075709822453136552357222532145366187415709}{10692676939101304445551066258002740418827890543478941138357697445728938303136362510196332}\cdot t^9+\frac{30928514857651563451634800180051795114696677243745198659450745243947328378057219555245}{21754066876102653871983203766281437403822260071215776798727729286138184823622254762123572}\cdot t^7-\frac{394257050188582586064909575819818827368287082175931800970612064092725877376432551853}{8366948798501020719993539910108245155316253873544529537972203571591609547547021062355220}\cdot t^5+\frac{8272944725558005523871118714033390306822960778023780058538033463615145987863368282579}{11161509697200361640471382240084399037191882667308402403654919564503207136427726097181863480}\cdot t^3-\frac{3566737357166539268789964728497308202808639983786175327065370450384146326825291786453}{1015697382445232909282895783847680312384461322725064618732597680369791849414923074843549576680}\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.