Rule: Q[3, 64]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{67}-\frac{3325045664001969272516798384459213452}{387634576082751948649051473144961}\cdot t^{65}+\frac{1675362591306601761814320481020683746400}{387634576082751948649051473144961}\cdot t^{63}-\frac{17027865091987884770159010922287053226480}{12504341163959740279001660424031}\cdot t^{61}+\frac{3766236755589913175689976491594772077730100}{12504341163959740279001660424031}\cdot t^{59}-\frac{622350477444417968216260157059972742886386190}{12504341163959740279001660424031}\cdot t^{57}+\frac{79839613518984438345571389742274637775329251910}{12504341163959740279001660424031}\cdot t^{55}-\frac{8157594364551715076699611801030411257782298122625}{12504341163959740279001660424031}\cdot t^{53}+\frac{5406229451055712457131597134273161730410095810799025}{100034729311677922232013283392248}\cdot t^{51}-\frac{735515821199166540409097912831819098096159997140501875}{200069458623355844464026566784496}\cdot t^{49}+\frac{20731384622863950192101855210263244360896158779883571125}{100034729311677922232013283392248}\cdot t^{47}-\frac{41480717668805935837459393728657560588054537618930627625}{4256796991986294563064395037968}\cdot t^{45}+\frac{6536309135817896010086459882916175689548822635187275078125}{17027187967945178252257580151872}\cdot t^{43}-\frac{432627290017183060316452629226560004269845218970434609854375}{34054375935890356504515160303744}\cdot t^{41}+\frac{12043237254007207599775137280786120439422469395601363125678125}{34054375935890356504515160303744}\cdot t^{39}-\frac{563983759838195989168538452459186818951979614497758777674819375}{68108751871780713009030320607488}\cdot t^{37}+\frac{177499522576369162328425646041430582969430917203985802241399411875}{1089740029948491408144485129719808}\cdot t^{35}-\frac{5851735859431667109230479559488318432974841797307627603097939015625}{2179480059896982816288970259439616}\cdot t^{33}+\frac{20133624238531516302208892194264077027405205472411091135071961590625}{544870014974245704072242564859904}\cdot t^{31}-\frac{460371626394911459990331689038842563540249253943832089070259908296875}{1089740029948491408144485129719808}\cdot t^{29}+\frac{17376771221201731800193792321769199833132298677415534604135443350053125}{4358960119793965632577940518879232}\cdot t^{27}-\frac{268472452294299546285610544860240402232009412061606272552306446788659375}{8717920239587931265155881037758464}\cdot t^{25}+\frac{1680713083674926325366110967269190828673687815199548961410821477030859375}{8717920239587931265155881037758464}\cdot t^{23}-\frac{16840253918775913186633650415404168063420426029769606709615088985529453125}{17435840479175862530311762075516928}\cdot t^{21}+\frac{531743237099467287798402806679653295400060013232046119529889960330180859375}{139486723833406900242494096604135424}\cdot t^{19}-\frac{3242690695365758880202054485929899246689970989487547068887042354181123078125}{278973447666813800484988193208270848}\cdot t^{17}+\frac{3724644617885365053974736473915883784487695023381098274094141188843442640625}{139486723833406900242494096604135424}\cdot t^{15}-\frac{12478851611393638165784510872950121300027946431894948063571609240254398046875}{278973447666813800484988193208270848}\cdot t^{13}+\frac{58349427425155725296908116601838155345935153782143720579186777204560130546875}{1115893790667255201939952772833083392}\cdot t^{11}-\frac{89467598083401746862125487492302312452266617319389168717304022793919294140625}{2231787581334510403879905545666166784}\cdot t^9+\frac{40963493388697995034620659202464184376655800272551734215483322257858866484375}{2231787581334510403879905545666166784}\cdot t^7-\frac{19134676983046896161009243358080213126483362362028042297169962826667396328125}{4463575162669020807759811091332333568}\cdot t^5+\frac{52599453513911236492828910475681506763257525922927774822481923844893931640625}{142834405205408665848313954922634674176}\cdot t^3-\frac{865956555689817470964691287360177081281658185065030741737639414222807421875}{285668810410817331696627909845269348352}\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 Hermite (physicists') type can be downloaded here packed into a single file.