Rule: Q[1, 2, 4, 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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-\frac{3}{5}\cdot t$
• $P_3$:
  $t^7-\frac{77}{45}\cdot t^5+\frac{749}{891}\cdot t^3-\frac{31}{297}\cdot t$
• $P_4$:
  $t^{43}-\frac{14495289199434918665694985466195943482215240958873245750766923}{1349751720940467225558115320440664999592027687630546402040040}\cdot t^{41}+\frac{1434931466248608220775863347747481280670854192088644108071663063}{26725084074621251066050683344725166991922148215084818760392792}\cdot t^{39}-\frac{16797696597640088018863803143262153008841903097805757915410388617}{101231379070535041916858649033049874969402076572290980153003000}\cdot t^{37}+\frac{9617695654473275324085055982283740903402852786423112718944421528189}{27096265797879879553079165057846349866809955829183219020953803000}\cdot t^{35}-\frac{321834241915766474095077365742540159685984610670488918103689194318097}{577150461494841434480586215732127252163052059161602565146316003900}\cdot t^{33}+\frac{134001319469033423615699871575347108617139476900179197397110662014077}{201128191126990196864446711543014042420457535768437257550988910450}\cdot t^{31}-\frac{1666973838157466279744695886807294596785719748897014510618610365890021}{2695117761101668637983585934676388168434130979297059251183251400030}\cdot t^{29}+\frac{1156391324185527844521389964408021296325747553393553314128279251260457}{2558656102311710732262898039249735602943795233509866377705618417750}\cdot t^{27}-\frac{3918627921263837756175439352253201678325476928700193936552018417266051}{14972876450564825766575477414868823157967394329428106951018063333500}\cdot t^{25}+\frac{573482520630237389256843430755527234063633768959097987329287920001661}{4765280679049327157014456290297381978970492456148423603541401026140}\cdot t^{23}-\frac{110944742097492461914243262582536826224277964672285685755001334375618293}{2530364040575192720374676290147909830833331494214812933480483944880340}\cdot t^{21}+\frac{2121297902310611130828652488096349786099969308018344548688318892780823}{168690936038346181358311752676527322055555432947654195565365596325356}\cdot t^{19}-\frac{10856029475904649544991257288738293492847542541519623247533961680158403}{3865833950878766656127977665503751130439812005050408648372961582456075}\cdot t^{17}+\frac{2334198530964041289818042455871929795553616758133748821828405458644681}{4859032396756710658690501571660841341817629318600908894002378589806450}\cdot t^{15}-\frac{85437921457884075629355291337243735698890546829759997558695956382487}{1389079317942878866269714008621686846869898550967265480432318399119810}\cdot t^{13}+\frac{93514175851132306250640844165690077879455650784494928991175292308259}{16391135951725970621982625301735904793064802901413732669101357109613758}\cdot t^{11}-\frac{4212554208287793230699841164304313013133012341209206902300951175511}{11512578675932064048316563723759713951791468040345386332967827409492104}\cdot t^9+\frac{4193619899563437005958265576095658138426219763348016723922158756841}{276973997335277058789536914446384831891028256526200207916504698976010600}\cdot t^7-\frac{845085815265649297926551169432181661009559498219297833406945494039}{2334495120397335209797525421762386440224381019292258895296253891369232200}\cdot t^5+\frac{51706841639541023723263525591656620972738300298942373789991684573}{12606273650145610132906637277516886777211657504178198034599771013393853880}\cdot t^3-\frac{850677994857491343504965022938111357262825372183278198244371}{61026220989639883077694647954784375823292947807225025063760993840772460}\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.