Rule: Q[1, 10, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^{11}-\frac{55}{21}\cdot t^9+\frac{330}{133}\cdot t^7-\frac{330}{323}\cdot t^5+\frac{55}{323}\cdot t^3-\frac{33}{4199}\cdot t$
• $P_3$:
  $t^{57}-\frac{1145191119579130349824396454241293428457020448086072899933032683134603107639}{81212624344938087535739736367040095472922541379395648922824896295953868684}\cdot t^{55}+\frac{6537234559341074415993010453035238191631478585082616075667196203206474069142122765}{69417546422952314516311504276300293126721690237076363060220576832618416657941892}\cdot t^{53}-\frac{4877128938355358327348034715096048366616409281706566809401546132393296219927394885519865}{12309605254542865076233970118803502079282177164670040232379734227997725970702861882684}\cdot t^{51}+\frac{2532909517017789925275881500947114624620480870992353929637040150881155121041972207101025}{2149524315601340084591238201546526977207402026176264992653669349695121807466188454092}\cdot t^{49}-\frac{78335979671759599737322323196302179587626815346549034324606020763538894773513102220232756305}{29726802654765557162301781948324397963392272292391877608455090604887264686929011058754006}\cdot t^{47}+\frac{12722315577127961583926959625391326241430237543465326927776947541031327694415627367674986502765}{2764592646893196816094065721194169010595481323192444617586323426254515615884398028464122558}\cdot t^{45}-\frac{25690022384043038901319637743162648618920369894841486963683418318822075947785699417125019008775}{3993300489956839845469206041724910793082361911277975558735800504589855889610797152225954806}\cdot t^{43}+\frac{2602529929748083768932370393852224045424659308762613761843188462255843120965654885058413275284925}{355403743606158746246759337713517060584330210103739824727486244908497174175360946548109977734}\cdot t^{41}-\frac{2972475453195729133300849144281545542658962465428519145327046476574239429822553143752476243642783725}{432881759712301352928552873335063779791714195906355106518078246298549558145589632895597952880012}\cdot t^{39}+\frac{1435206732570635694941684134585972690696005762229825728099165860578896211693341082663313094320245}{268409742681880694451814525538756401373569002093884699668356500969301619012839616268197293612}\cdot t^{37}-\frac{1985162325173331691790088965606292683099922877691191577113975477277093188544264409654432466374515}{571230990835797375371810400505558495230928901892113591601886912319282932770915080775907060764}\cdot t^{35}+\frac{9555160945475659005347427467492236668925090322316936407720687153713580704362436465926869348046325}{5054674229832728035853078585986160466203093560440299260141066543463906959729189748378404495668}\cdot t^{33}-\frac{924454416337604988547021662739344379991750170731756564332227467327064878808876464404145215804575}{1073438882141896545248368839497060959220549438910708713847161981004431854351091371295413857951}\cdot t^{31}+\frac{1056991089645531679261705688428119109857432276360515628340733169632766718830770458945588181961725}{3220316646425689635745106518491182877661648316732126141541485943013295563053274113886241573853}\cdot t^{29}-\frac{34758798697673508170581049394618210798082697583149307725926576353048921727972363775646032493565}{333136204802657548525355846740467194240860170696426842228429580311720230660683529022714645571}\cdot t^{27}+\frac{173571934319288051707384259416715357578410036481828973949095701833726536044756279924556079993470}{6304911135339185455424327321643656898410353600958300606619537612566260661763306790022488292103}\cdot t^{25}-\frac{824674715732590717909690019341050610470149219135386147888725736373276016927299834740973996894375}{137738058648948359180039150718984504549887724820935182483072975536062925226213779105106667304404}\cdot t^{23}+\frac{5712132470805432766726060516764280970501775794390433171575807631261226670648200380613758978954625}{5371784287308986008021526878040395677445621268016472116839846045906454083822337385099160024871756}\cdot t^{21}-\frac{38973393414219001577105839235417918076722428465599056826303232695032006806842795460596760925975}{255799251776618381334358422763828365592648631810308196039992668852688289705825589766626667851036}\cdot t^{19}+\frac{5731389213074759946074649745288321645633401678598747978217962367200795763327921481678989228285}{330594354635278726753761470355591045590499108947825212425955437523064982602265820692540898216836}\cdot t^{17}-\frac{134330633266623545698217911458549459035894273537365109040359841392092689565424613152335204835}{87510270344632604140701565682362335597485058250894909171576439344340730688835070183319649527986}\cdot t^{15}+\frac{25916582788501904996182649552997769389713867607460497003754959150555344993245933561011799912525}{251682778632287244790292543701203053561166934383583051181497231274299657784448507590567434992470254}\cdot t^{13}-\frac{105497217747232658503694478528200466866232220229903561128012136331048754125473258618476212558325}{20892168718575447146326690978750237594991854729364773724999074138509048267650510978727673456087115154}\cdot t^{11}+\frac{489211294914634053749848085299631614483334160992119709211394391121254243102087337949746216906025}{2839727855824831931350712535342436140796200562060581167082566461749652945302957915339369153608148652086}\cdot t^9-\frac{31214879900965323170887080888281438080792455956051061962210853505842687213976374507137449127743}{8203658250160625579457613990989259962300134957063901149349636445054552953097433977647066443756873883804}\cdot t^7+\frac{56956682688471396172707983912612622890259451992335339357914802015329799646818995928517135929}{1171951178594375082779659141569894280328590708151985878478519492150650421871061996806723777679553411972}\cdot t^5-\frac{17551636388803838277460724728779531244705769656474385295728387098203848079618743747861190905}{59769510108313129221762616220064608296758126115751279802404494099683171515424161837142912661657224010572}\cdot t^3+\frac{127168850759172387695100234492750332650299970807995947919874340412460674578865440552885}{240038193206076824183785607309496418862482434199804336555841341765795869539856071635112099042800096428}\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.