Rule: Q[1, 2, 76]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{79}-\frac{977541230480659354111415737264472376276046879}{322267141690365338018541861245032759709743}\cdot t^{77}+\frac{1407665532415662437915410952048277273493767466225}{644534283380730676037083722490065519419486}\cdot t^{75}-\frac{34629706115953006019145517011965786512391958711825}{34839690993553009515518039053517055103756}\cdot t^{73}+\frac{22382527466434994366396584466330089260147903114592425}{69679381987106019031036078107034110207512}\cdot t^{71}-\frac{10940628993300365297772638435131932420482181809691365025}{139358763974212038062072156214068220415024}\cdot t^{69}+\frac{4206042457790972512619454186684643897160304606629245276575}{278717527948424076124144312428136440830048}\cdot t^{67}-\frac{1305847863287788764359068959101357800543371473407789693933875}{557435055896848152248288624856272881660096}\cdot t^{65}+\frac{83407166252922594416521127763264571544867837751338090936692875}{278717527948424076124144312428136440830048}\cdot t^{63}-\frac{17779726042094145455485501781132172273808386951663857833587400875}{557435055896848152248288624856272881660096}\cdot t^{61}+\frac{3195197752336648089833223147287375651595622919365585037905977961125}{1114870111793696304496577249712545763320192}\cdot t^{59}-\frac{487900304388889599764168880983796511144659651497518771078745884799625}{2229740223587392608993154499425091526640384}\cdot t^{57}+\frac{63680682229718756331203671517493775109565400171104481472310217832383125}{4459480447174785217986308998850183053280768}\cdot t^{55}-\frac{7136067431072081992480979197557829395521787233781758853142587768063688125}{8918960894349570435972617997700366106561536}\cdot t^{53}+\frac{688787546446759181227343481064334476718668283954926497907472892842006911875}{17837921788699140871945235995400732213123072}\cdot t^{51}-\frac{57390484452986706252984313680226249820925969794276260753656727120762618584375}{35675843577398281743890471990801464426246144}\cdot t^{49}+\frac{8266402036325835668941731426087658160752474911500414070221203977443333499928125}{142703374309593126975561887963205857704984576}\cdot t^{47}-\frac{514835969974452834453473235836341427250174569209696320719818438979615387968078125}{285406748619186253951123775926411715409969152}\cdot t^{45}+\frac{27721431222498484748886135827995103118252238150522058894179929318411022486004671875}{570813497238372507902247551852823430819938304}\cdot t^{43}-\frac{1289240859950055970176663844607750486693874848423330031281008925111984650857359859375}{1141626994476745015804495103705646861639876608}\cdot t^{41}+\frac{51700353244822410561959519112579608185368652673514210647188862219417936870337668109375}{2283253988953490031608990207411293723279753216}\cdot t^{39}-\frac{1783404616318293429661275383895948180689034832961850976132645793111913179244903535734375}{4566507977906980063217980414822587446559506432}\cdot t^{37}+\frac{52750994370597349064274460171352273578149653769077037802447578975044084624903853817265625}{9133015955813960126435960829645174893119012864}\cdot t^{35}-\frac{1332630998643850713697295989939832285996668186594158425604731361917383991977480175554453125}{18266031911627920252871921659290349786238025728}\cdot t^{33}+\frac{14306783789488209195876323003828456788927157326001519606042376727762294176983010678110859375}{18266031911627920252871921659290349786238025728}\cdot t^{31}-\frac{259556054646429526064132456200728906833171941550091715466048377624460578625175553307282859375}{36532063823255840505743843318580699572476051456}\cdot t^{29}+\frac{3950784919546215946172919755356957617741280587524669134670833482065086505259140224949681390625}{73064127646511681011487686637161399144952102912}\cdot t^{27}-\frac{50030528814976420809477025030532929974139391140972779261833849875926751675827008527313295703125}{146128255293023362022975373274322798289904205824}\cdot t^{25}+\frac{521794860812700367700422427586700831260451442615623497567287833767936201249484222824436428515625}{292256510586046724045950746548645596579808411648}\cdot t^{23}-\frac{4427921737607916835148126544619369448597162871155566216207074905469556215649535125312236669140625}{584513021172093448091901493097291193159616823296}\cdot t^{21}+\frac{30125431964466271857679008891704028412696159338513471365117436483366372797961196629472109405859375}{1169026042344186896183802986194582386319233646592}\cdot t^{19}-\frac{161376626191315758827545598937206209263589759258012724066783697273040022799039861363894003994921875}{2338052084688373792367605972389164772638467293184}\cdot t^{17}+\frac{2661817202740108306901941368762313998971479711641508061548181582859294784081123073408672844123046875}{18704416677506990338940847779113318181107738345472}\cdot t^{15}-\frac{8209828327997700452795114949611298674197061186944363044421491902062892847295445238826378791966796875}{37408833355013980677881695558226636362215476690944}\cdot t^{13}+\frac{18238781944822348393460206729443506170401116000040668385563487654369115950314219356739008402564453125}{74817666710027961355763391116453272724430953381888}\cdot t^{11}-\frac{27725110039097015167269016835534656945373765838790573362553986191168641461577916234990526393322265625}{149635333420055922711526782232906545448861906763776}\cdot t^9+\frac{26789277022044625716243423096229518480117206534660096404936777496900100715519202052248325296900390625}{299270666840111845423053564465813090897723813527552}\cdot t^7-\frac{14673576327157755718096605851227350819245232211922216443073268779871966469153249871881854275947265625}{598541333680223690846107128931626181795447627055104}\cdot t^5+\frac{3721691541584187646500974025391209619784394356005561822786270001960337152855172456771282967177734375}{1197082667360447381692214257863252363590895254110208}\cdot t^3-\frac{275531971434859724601433132424004904678464876391094198585068486538999916853159125497568750498046875}{2394165334720894763384428515726504727181790508220416}\cdot t$

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.