Rule: Q[2, 6, 8, 13]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^8-\frac{161}{52}\cdot t^6+\frac{105}{52}\cdot t^4-\frac{245}{572}\cdot t^2+\frac{25}{1716}$
• $P_3$:
  $\frac{3}{2}\cdot t^{16}-\frac{52675}{9724}\cdot t^{14}+\frac{62424565}{7972932}\cdot t^{12}-\frac{25786918405}{4472814852}\cdot t^{10}+\frac{2493674299078805}{1096541870671764}\cdot t^8-\frac{66130895817287}{143027200522404}\cdot t^6+\frac{613871878555495}{14255044318732932}\cdot t^4-\frac{244523487906245}{156805487506062252}\cdot t^2+\frac{24672636591575}{1411249387554560268}$
• $P_4$:
  $\frac{3}{2}\cdot t^{29}-\frac{7048867702224628775616014042054054330493382674323507434126245274391204753527121458823922502765219}{686491396855073959322745543789200029445735675198285370391246822151282347990542438475673968586908}\cdot t^{27}+\frac{229404100270727253066250274382435952814686778621081538895392531668818283595156979318360214532653097775}{7317311799078233332421144751249083113862096561938523763000299877310518547231191851712208831167852372}\cdot t^{25}-\frac{41198760550648073114147639130456416958584970408706993257997661852053830660721854248001035893561932052587200}{731718374612174946333782738121593625490760397524868983883444737206266561315661530585480386751330693458349}\cdot t^{23}+\frac{1030098303611308111214537073546719230314655786730905249353590397811461669356879509006494912429751787870330130625}{15598772309982345505943580411276132908212030154435156998427274907763190554127272509021270884764867723145083982}\cdot t^{21}-\frac{54666023935327419742473098646531125191937422819294058856961406994152653461184923216017370805855188492592815945575}{1029518972458834803392276307144224771941993990192720361896200143912370576572399985595403878394481269727575542812}\cdot t^{19}+\frac{4748137913426729136518830729320148070214982688202320105109896003481073162212147274991900143073982228621673332544375}{158828888961617081568956966425566045079542359387568162965986292377498527371675345146154091905993043138498072484932}\cdot t^{17}-\frac{39855465117540540864881370581861310414695607860058520501433572801426136183659074357338048089335172734632824000}{3370445822969550156373757881876878980552210325684750084160646218009899995154811670192557760504054051831297693}\cdot t^{15}+\frac{4509068093581343245016639580979160523303485697781817163039872089149236131871814326045202616278062098813713138376625}{1387417059458831565470006442011562217312472962885521894144056730474031253805516985541404861649409818003939044941906}\cdot t^{13}-\frac{43037678536496993830772322050788220079764098372335495636676055989035249322085841497135777907814340245219426294625}{71149592792760593101025971385208318836537075019770353545849063101232371990026512079046403161508195795073797176508}\cdot t^{11}+\frac{10870463731972288429662465568932318865165356987186522286749698619723557707103331734414688126444929657266776638771}{148767330384863058302145212896344666658213884132247102868593495575304050524600888892551570246789863935154303187244}\cdot t^9-\frac{2900399068307227024361728887594557293067924154313010294785778453017821146393172373042045486607922630151849072}{539012066611822675007772510494002415428311174392199648074614114403275545378988727871563660314456028750559069519}\cdot t^7+\frac{104556895407072292861727411717477372956192135858803352323808645510600904235498154782879134680680571646140069615}{471096546218733017956793174171758111084343966418782492417212735988462826661236148159746639114834569127988626759606}\cdot t^5-\frac{5962520282881520185166795446153857372336007854449575982024692516249231883747919491283034572323763178703206735}{1298698586873263995448456858527549387313596880397724708825829704616843468093137489521463707830084487866347025121076}\cdot t^3+\frac{9710932380810052651986958017509606171267818920961386072930388466438023475289589465150442868307168669726563725}{267717437265445706490303320979321966556217185487702393547953180537443589208342485339924590056973130855876965321387524}\cdot t$

Warning: This rule has negative weights!

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.