Rule: Q[3, 78]

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^{81}-\frac{24683935653411356689598626285428169885538868951}{1920479133419531540463967153934194548708913}\cdot t^{79}+\frac{37709070306935453099075119033166469355717652262591}{3840958266839063080927934307868389097417826}\cdot t^{77}-\frac{1919483603975923175848275786046383274141817414516547}{404311396509375061150308874512462010254508}\cdot t^{75}+\frac{1320369234210854582998669976570715902941276771440186975}{808622793018750122300617749024924020509016}\cdot t^{73}-\frac{688061235066689590422765838126113592005168549195683432775}{1617245586037500244601235498049848041018032}\cdot t^{71}+\frac{282518159261817119978875896728024563329939839649362568308775}{3234491172075000489202470996099696082036064}\cdot t^{69}-\frac{93861546446060426678637374617174981596590826333865899757205025}{6468982344150000978404941992199392164072128}\cdot t^{67}+\frac{25713695026631312056739145434221260753590973400682205769491045825}{12937964688300001956809883984398784328144256}\cdot t^{65}-\frac{1472547853355665590987593439831423189286729081126439579629329721125}{6468982344150000978404941992199392164072128}\cdot t^{63}+\frac{285023856840215254591509480518401191391875835234689289900279227982125}{12937964688300001956809883984398784328144256}\cdot t^{61}-\frac{46990925981247845931959071899548867642397988190314038337734469219474875}{25875929376600003913619767968797568656288512}\cdot t^{59}+\frac{6639285506954759291376441702327552677214400662737942081996512054907592375}{51751858753200007827239535937595137312577024}\cdot t^{57}-\frac{807631019163760622635323048857885321412411809915929047652538266174897990875}{103503717506400015654479071875190274625154048}\cdot t^{55}+\frac{84874333193953850735330623601013806382277239264424909445098071956914961776875}{207007435012800031308958143750380549250308096}\cdot t^{53}-\frac{7724341373857795723117410316438858265180592099015750561651644657923466093008125}{414014870025600062617916287500761098500616192}\cdot t^{51}+\frac{609733741020597784832507522783271339665898551090504643056709794336961816515334375}{828029740051200125235832575001522197001232384}\cdot t^{49}-\frac{83556049162682036261578515212585610084524371186570987760070786620574279553299121875}{3312118960204800500943330300006088788004929536}\cdot t^{47}+\frac{4969815939789063547869243076328858603562044711310486742177256074618724211339608146875}{6624237920409601001886660600012177576009859072}\cdot t^{45}-\frac{256442666200793966255207929956150662498813265236693982749260968906254218295317096828125}{13248475840819202003773321200024355152019718144}\cdot t^{43}+\frac{11465019190317934258401414935709589755678729665162319713562998089532385166774319382890625}{26496951681638404007546642400048710304039436288}\cdot t^{41}-\frac{443254982922353198624369395418912439124740625333718238424639429286517226169636138670140625}{52993903363276808015093284800097420608078872576}\cdot t^{39}+\frac{14780533805386348557354451474007645028343437278116992017091946794574288393541134121775140625}{105987806726553616030186569600194841216157745152}\cdot t^{37}-\frac{423675432867515257874301982487577525153916677770747788728996645610144223055843758999905734375}{211975613453107232060373139200389682432315490304}\cdot t^{35}+\frac{10396584178484500480428979664999977116088850689104975635687703684897996600235323306868813359375}{423951226906214464120746278400779364864630980608}\cdot t^{33}-\frac{108657629524877155635167791509551720606501140313515314336472980004309930600950132134894016890625}{423951226906214464120746278400779364864630980608}\cdot t^{31}+\frac{1923084942619440906984907090648738943584744925684160383516883508834042805888003512284723638015625}{847902453812428928241492556801558729729261961216}\cdot t^{29}-\frac{28613526254387575806128249485310409179002542152785523964708989663092079657769451147590376064109375}{1695804907624857856482985113603117459458523922432}\cdot t^{27}+\frac{354880467979809611029846125508709396407839316910515689965128556566591499652759720277488308412796875}{3391609815249715712965970227206234918917047844864}\cdot t^{25}-\frac{3631758063391366666152845120373314991505828615034911228978205835954607396802019821207557859340234375}{6783219630499431425931940454412469837834095689728}\cdot t^{23}+\frac{30295391152341798829840837207180437928737384992544995983532109187808751858653305847515334964858984375}{13566439260998862851863880908824939675668191379456}\cdot t^{21}-\frac{202974863023143391702466545768859454197189652246518404082680107206582776803161656535414700527394140625}{27132878521997725703727761817649879351336382758912}\cdot t^{19}+\frac{268153226182150262815011555980745566375414616440347105422363018061990504138830561896217483972617578125}{13566439260998862851863880908824939675668191379456}\cdot t^{17}-\frac{17483482228376972851268486153882735500441639141447321276659781301704440661981808176481453206536270703125}{434126056351963611259644189082398069621382124142592}\cdot t^{15}+\frac{53380465886412415161601398160362397515691468525792718182130821795016206240547169234374955421776017578125}{868252112703927222519288378164796139242764248285184}\cdot t^{13}-\frac{117596866900104237281718415329632397205555062598614299144687621798156797376664854330875346046695748046875}{1736504225407854445038576756329592278485528496570368}\cdot t^{11}+\frac{177575983264041311501068175326293685634183008753185945004528665414511226292232010443175812317745646484375}{3473008450815708890077153512659184556971056993140736}\cdot t^9-\frac{170747111229871388583307994063874689712314815873124367226168775971518498306057777397581471738092443359375}{6946016901631417780154307025318369113942113986281472}\cdot t^7+\frac{93238668210245310358216985937825918544448697901441459634454201142510141743020189317781431698990005859375}{13892033803262835560308614050636738227884227972562944}\cdot t^5-\frac{23619766856621757267037942347728753882722603962037376656335863639871000729030506496640876535919697265625}{27784067606525671120617228101273476455768455945125888}\cdot t^3+\frac{1749913716757776852397672391816506956553607942354809197787798754778531998911880026077257793868916015625}{55568135213051342241234456202546952911536911890251776}\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.