Rule: Q[1, 16, 36]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{17}-\frac{136}{33}\cdot t^{15}+\frac{2380}{341}\cdot t^{13}-\frac{61880}{9889}\cdot t^{11}+\frac{77350}{24273}\cdot t^9-\frac{12376}{13485}\cdot t^7+\frac{43316}{310155}\cdot t^5-\frac{1768}{186093}\cdot t^3+\frac{221}{1178589}\cdot t$
• $P_3$:
  $t^{53}-\frac{1741459732289057171770264982980751745245011648855015452358382665481939115597503302}{130302818179898099765389921488278699490390907148459289744658619797341315073157019}\cdot t^{51}+\frac{2609340843897827668848405352816249162318658950192360577569422394126361149847404314565439}{30964597066725538203148277586148100939198703480828888957998447554621068301619716981411}\cdot t^{49}-\frac{1290143235825280707842009019144787345872143628600842265375641161375099012200555793032384568}{3870574633340692275393534698268512617399837935103611119749805944327633537702464622676375}\cdot t^{47}+\frac{474756904606496288537236123216959674989590384751798701999050826511243685723793929797171386384814}{511763507445672991960257764270364469759989171941464358642199592153055378721482169945647626125}\cdot t^{45}-\frac{212335160046743803995398634405835262290843588871941238789894920871273101051846980754902694444892}{109934383080922346421092408621041256466960636935573825189805838314360044317948021692028008575}\cdot t^{43}+\frac{61746120873466215978122028363349614284979030819988265230715821141699164796993444402613633264165052974}{19775326631745554441265365739978764337046280253881826396617843613502027852045443986027074266496725}\cdot t^{41}-\frac{524048404207509926836412066924158891408984682049778710362832483194179164545946717377870167495810899176}{130517155769520659312351413883859844624505449675620054217677767849113383823499930307778690158878385}\cdot t^{39}+\frac{33178081114753032447355221625058687918552113849074327255866623165910226060883067530127388649666470412883}{7948160126990040150431656614722234127774370332810195609409864067734468886687495755922420234034260625}\cdot t^{37}-\frac{6173760162289972382140573326416781968515982433309405981575382679497952186390048484237517904035804566467834}{1740647067810818792944532798624169273982587102885432838460760230833848686184561570547010031253503076875}\cdot t^{35}+\frac{83556169098451041541796314236860909004852435928806236887677072973774127644780698913531252478780560333669}{33689943247951331476345796102403276270630718120363216228272778661300297151959256204135678024261349875}\cdot t^{33}-\frac{1462743415397606971710373993406323727988511230188101742535998684012805031950117849413085072563727079472}{1020907371150040347768054427345553826382749033950400491765841777615160519756341097095020546189737875}\cdot t^{31}+\frac{110880289707295425361894583790632787431877961553435825706233834993753839880481730145898834732340836724}{161937031285868468956312081578949917288298122626615250418030075069990978995833415401279121119751525}\cdot t^{29}-\frac{9852158392018737513399042308640772351385908638057275234016328684460113828805586357702218788929497570008}{36435832039320405515170218355263731389867077590988431344056766890747970274062518465287802251944093125}\cdot t^{27}+\frac{118684538020004785101926362382488740598828491984952420314704081647125373814596686559840725360645720668}{1349475260715570574635934013157915977402484355221793753483583958916591491631945128343992675997929375}\cdot t^{25}-\frac{43601920806816833221322362304689131581832236413732599236725517031018106536393750516932440356890627728}{1861102403039039070758775082494308469704643641201534689586925355514534004981099977003106420984970425}\cdot t^{23}+\frac{10171273171957089817371210064522149913077054283642178733562849572889996686829562915095570648739854693543}{2006437581603633121829846700300000376566124449182636353073758890095168978642805875207258095132796751825}\cdot t^{21}-\frac{24630783682839499526818296157045375890425658651296262695644575685339845155113425289792016251066193302706}{27956363637010621497495864024180005246821333991944733186161040535326021102423095194554462792183634742095}\cdot t^{19}+\frac{696234054709759373746565094607216513954893366114580117111426074768353303605279675311805636881677984194607}{5745768421185604049880071000759101078359858380976009636418887541602532231840115091301851431761952298309525}\cdot t^{17}-\frac{222905772623254746994758258968193987028863745290742708142556142383724409395229698958775860041403220888472}{17237305263556812149640213002277303235079575142928028909256662624807596695520345273905554295285856894928575}\cdot t^{15}+\frac{19655299675880337967379351325925805159453264202176384324547250728104163311812988677412471292352386542}{18838584987493783770098593445111806814294617642544293889897991939680433547016770791153611251678532125605}\cdot t^{13}-\frac{5431672927550057516287789074918491687291151114201578759381923431715287408665930828531814215433500276}{88396437249009293075078015396293862743997821245784763637213654486192803566771001404643868180953112281685}\cdot t^{11}+\frac{36387774036058462404841002254676942458586593404289947716337056248268833628621116616183303162739714}{14464871549837884321376402519393541176290552567492052231544052552286095129107982048032632975065054737003}\cdot t^9-\frac{13392963726545124315604760981403565924295197990095123205605516330507549362836944930487959557803192}{200900993747748393352450034991576960781813230104056280993667396559529099015388639556008791320347982458375}\cdot t^7+\frac{205371442610088581232293365653129293896676435650561290324847319377515316456814443740759379047139}{200900993747748393352450034991576960781813230104056280993667396559529099015388639556008791320347982458375}\cdot t^5-\frac{15172801718662442107424294856560911851598640990164269467199776050889766131082775901591295958}{2043060953366932813753729169405867397781151492583623196545770134503685752698867520908563979528962533475}\cdot t^3+\frac{648928115361990566194875977201477075887663072535332753400091746138004898808142354984375211}{40180198749549678670490006998315392156362646020811256198733479311905819803077727911201758264069596491675}\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.