Rule: Q[1, 2, 4, 44]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{51}-\frac{87157768709928771194357939184929783610143786534267915126581749199354139}{6726819246303990742337927631392683227724879224498584138170345119954315}\cdot t^{49}+\frac{86534408076692623143295158039635061927040319787092768189906910573952394490338}{1094164238146068222176460294739439675772045680019266200162373826176409014955}\cdot t^{47}-\frac{64509108261488051846878519642003429564909605350162066713289155779544636054718726}{213362026438483303324409757474190736775548907603756909031662896104399757916225}\cdot t^{45}+\frac{31142883474897250869588692403531909926750526472126585829685860730620566855358332}{38362061319242452516914077606470657723280510660069424048117167178366825160695}\cdot t^{43}-\frac{14718604435734436266243148852788775932179852418042330009434199260082725988171892}{9044713644374236772280554882826415235570201700341571523539819903842584793985}\cdot t^{41}+\frac{7093107750982415701726056343754103533176495414898579405084730360297006257468906}{2806980096529935550018103239497853004142476389761177369374426866709767694685}\cdot t^{39}-\frac{28385821024892698591938846909741346659177160470974174893604315231612358724651054}{9117950192101963385821288120744038030999919932733001252475365004278557140495}\cdot t^{37}+\frac{1268471029082309045353506992530806553219635026721248771918608772315274175984500247}{410307758644588352361957965433481711394996396972985056361391425192535071322275}\cdot t^{35}-\frac{3740702705370324148531084593005615739868063705028667947887807854242272629893809163}{1496045212288729838612062120119002547701756093578422436271534888778935567744295}\cdot t^{33}+\frac{10746166402203951411123632483947631995165192426288823111856925982850493867091894396}{6482862586584495967318935853849011040040943072173163890509984518042054126891945}\cdot t^{31}-\frac{2834556892186545746298240216293227621280949011545874575154796922037259658493443964}{3136868993508627080960775413152747277439166002664434140569347347439703609786425}\cdot t^{29}+\frac{9599503065405430786196876212602208950080374615053064121509023105379854221656725776}{23688769295806528645876200533808677715833701882190037130506450658251554846318175}\cdot t^{27}-\frac{39317137410676435781073764774918056154112213731720740465203928412872477310031960464}{263545994587249271687027245255050958633420529487043005682699970998496642948354625}\cdot t^{25}+\frac{2050062959169007357087042978366644120610640279884586143227046246637912778437142172}{45681305728456540425751389177542166163126225111087454318334661639739418111048135}\cdot t^{23}-\frac{27420718466730504732756079416834828137727175421907754804920396213689483330987321692}{2504166123114481261520735243096175108760464885635066813995981906251169920087456855}\cdot t^{21}+\frac{23271377079655981912440393006389403331774951210116874615802286512670252757211776883}{10851386533496085466589852720083425471295347837751956193982588260421736320378979705}\cdot t^{19}-\frac{721317851437026635219444189803616575559175275457004181351858953425295309705849351}{2170277306699217093317970544016685094259069567550391238796517652084347264075795941}\cdot t^{17}+\frac{397087221875781433935863633249489727425003559027324537174576104555468119138566133738}{9929018678148918201929715238876334306235243271543039917494068258285888733146766430075}\cdot t^{15}-\frac{142251514313177866301968964992863619601382882495762868728510653794741541720184701266}{39054140134052411594256879939580248271191956868069290342143335149257829017043947958295}\cdot t^{13}+\frac{585023109354283732442424041598322857235515969125280138209596530722123735730224828}{2411794136122413283719005586734641550875342948515654983209285052554383807119723763405}\cdot t^{11}-\frac{1156311773100051641927966103966953883804753242226485190558865629603383057720257420}{102742430198814805886429637994895730067289609606766902284715543238816750183300232321053}\cdot t^9+\frac{78875191096680075457068028378845809324927663617271680652141683793443768606621514}{232707213698170286836785077509806568101126038852933582097859991096465288876705654402385}\cdot t^7-\frac{9959897953242369057127554134039525754728531395041647493140635853270469673856378}{1680663210042340960487892226459714102952576947271186981817877713474471530776207504017225}\cdot t^5+\frac{4919343983943102954468925253149049590545009521558149302125725159088398397675803}{99831394676515053052980798251707017715383070667908506719981936180383608928106725738623165}\cdot t^3-\frac{4099417174662853911847807282507809633367099946261884062700565068421535260777}{33277131558838351017660266083902339238461023555969502239993978726794536309368908579541055}\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.