Rule: Q[10, 52]

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.

• $P_1$:
  $1024\cdot t^{10}-23040\cdot t^8+161280\cdot t^6-403200\cdot t^4+302400\cdot t^2-30240$
• $P_2$:
  $1024\cdot t^{62}-\frac{88437343954737973965627027496681971519955707737968788538868579206267392}{101475461435436910237680420608352651643167018189549275622186873811}\cdot t^{60}+\frac{35068473476588589116561335373086070928450403135860602202527786155104288000}{101475461435436910237680420608352651643167018189549275622186873811}\cdot t^{58}-\frac{94789806804995861830542076945048954662621926168472817833641447124741637722240}{1116230075789806012614484626691879168074837200085042031844055611921}\cdot t^{56}+\frac{63308232108104430303808866984399424970323494317531215394229803168188491828072000}{4363444841723787140220258086159164020656181782150618851754035573873}\cdot t^{54}-\frac{87990434369128144687137598325424154891413011973521742661059590974111864293141100320}{47997893258961658542422838947750804227217999603656807369294391312603}\cdot t^{52}+\frac{8538284123657420628277617559278514828943232400295716168299803925358887076511073258960}{47997893258961658542422838947750804227217999603656807369294391312603}\cdot t^{50}-\frac{652302804190751483830285758340654087945128176852810521084934535413329023280219288935000}{47997893258961658542422838947750804227217999603656807369294391312603}\cdot t^{48}+\frac{39908232192356241694076459290543970134332216111634069635376100510518464197921141234113500}{47997893258961658542422838947750804227217999603656807369294391312603}\cdot t^{46}-\frac{86024690427050822417447854822023180094926266105359715040026034712528838937883941710793750}{2086864924302680806192297345554382792487739113202469885621495274461}\cdot t^{44}+\frac{7366641037242394839892891233352775229242284593343933102331161307408895306742373742222375}{4411976584149430879899148722102289201876826877806490244442907557}\cdot t^{42}-\frac{490192880626596863663520488275717975785506381146488855523874211172182443210375650287743625}{8823953168298861759798297444204578403753653755612980488885815114}\cdot t^{40}+\frac{26878676635470392985961653312668887873738371081389494712728198354373198990992302193204490625}{17647906336597723519596594888409156807507307511225960977771630228}\cdot t^{38}-\frac{1216108737650271487985181857741003590141739148221253358101256426732439457190096633232082781875}{35295812673195447039193189776818313615014615022451921955543260456}\cdot t^{36}+\frac{45387024344909422387230270908445836871936626046204325655933480986309260763023423560086058859375}{70591625346390894078386379553636627230029230044903843911086520912}\cdot t^{34}-\frac{1394757586110965916803920354147297997651503047076310979372041088632959499358724871614611451325625}{141183250692781788156772759107273254460058460089807687822173041824}\cdot t^{32}+\frac{35175895699066884606633642672883126917142834904682392506918352678482786769463569838560143636719375}{282366501385563576313545518214546508920116920179615375644346083648}\cdot t^{30}-\frac{724583159011489046182767925017490237996210174527250636844582824260153057988485397049910412274203125}{564733002771127152627091036429093017840233840359230751288692167296}\cdot t^{28}+\frac{12112867882463018807217621517843256755119166990641116929880064627182694445248327017637868125624290625}{1129466005542254305254182072858186035680467680718461502577384334592}\cdot t^{26}-\frac{162990866372126975738617598841460071856308822543503899388408739729661411295451105310280479146849609375}{2258932011084508610508364145716372071360935361436923005154768669184}\cdot t^{24}+\frac{1747339300379341849555913465298996237804046959118564614909904733224304302211328611138969879881954734375}{4517864022169017221016728291432744142721870722873846010309537338368}\cdot t^{22}-\frac{14734604769531831025120213321775826244688557867243615612837505121174692026730588509766538893592095203125}{9035728044338034442033456582865488285443741445747692020619074676736}\cdot t^{20}+\frac{96187995731369364582769761159115962481988466861235162773966162292452864576064026263323424451421503515625}{18071456088676068884066913165730976570887482891495384041238149353472}\cdot t^{18}-\frac{476416953982346333374280400802081513522573020368376073781847667386163319964768949370979520784331782109375}{36142912177352137768133826331461953141774965782990768082476298706944}\cdot t^{16}+\frac{1744670961858846666358167366217680648982873901547990063454214950153397625556962084992047344662318138671875}{72285824354704275536267652662923906283549931565981536164952597413888}\cdot t^{14}-\frac{4565854350926319628486257332059919198158310547808245694081831274094936965714874181368416693205039638390625}{144571648709408551072535305325847812567099863131963072329905194827776}\cdot t^{12}+\frac{8153929335856065225860478158689508724892463147476812202546316596095284146100010210713785817471267945578125}{289143297418817102145070610651695625134199726263926144659810389655552}\cdot t^{10}-\frac{9313804694797647552241053246381048885017921796295129608379870075855675448459420976372221918498633701171875}{578286594837634204290141221303391250268399452527852289319620779311104}\cdot t^8+\frac{6192593075976735294765326912462689173696793482082832330122283031918102074603500872016849641779727381796875}{1156573189675268408580282442606782500536798905055704578639241558622208}\cdot t^6-\frac{2075939214028246177646325399533159116635895508239832332901722226051742460172745655591161156428541369140625}{2313146379350536817160564885213565001073597810111409157278483117244416}\cdot t^4+\frac{274591347976453695623915472153995092028901194403164022194310349231035450499083665497307910319311949453125}{4626292758701073634321129770427130002147195620222818314556966234488832}\cdot t^2-\frac{6977984422267839807015969524030087277670123576645954116060601956714911016648503989842375111068104921875}{9252585517402147268642259540854260004294391240445636629113932468977664}$

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.