Rule: Q[6, 63]

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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{69}-\frac{266829227512486179953432993409618144707194042608730509220275888197365079727711072}{3873083718309467034356100955213777793878106552535640935627498330485698046729}\cdot t^{67}+\frac{3915613215145093893534949162350400871294709293240450117433391610287620077453261297520}{112319427830974543996326927701199556022465090023533587133197451584085243355141}\cdot t^{65}-\frac{23549790872111200471830389726456896632298494812379304906276901863416802871989744805088120}{2134069128788516335930211626322791564426836710447138155530751580097619623747679}\cdot t^{63}+\frac{5235267336337784358682820356965526946362800538000408759704257854399360387964107998324258780}{2134069128788516335930211626322791564426836710447138155530751580097619623747679}\cdot t^{61}-\frac{869917742441580776935955009666072546259729035803289751249695641740332603697606009051857361930}{2134069128788516335930211626322791564426836710447138155530751580097619623747679}\cdot t^{59}+\frac{65623398166113882308687103516679061615508591558449821721455152323562326515956965982944659335}{1247264248269150400894337595746809798028542788104697928422414716597089201489}\cdot t^{57}-\frac{710548384035530972578111729872179354787751955370958247960382904373915113364242517194345778475}{131290973502015831673088167973348399792478188221547150360254180694430442262}\cdot t^{55}+\frac{118600623045834113409360184843340531122879452242659636794556385532631163253759409240174341643575}{262581947004031663346176335946696799584956376443094300720508361388860884524}\cdot t^{53}-\frac{16268855742259943063951420898217647663635495432138630762806695147844178667506457467833414720165725}{525163894008063326692352671893393599169912752886188601441016722777721769048}\cdot t^{51}+\frac{1851107335829780741037918577271834803226690469136464701486093635238031743612015164868987022717653625}{1050327788016126653384705343786787198339825505772377202882033445555443538096}\cdot t^{49}-\frac{175871995041433398851181832277187821236079229073968668682911300465502502486772431940142809974646406375}{2100655576032253306769410687573574396679651011544754405764066891110887076192}\cdot t^{47}+\frac{14016900403198505933534170909605896437861722928851087328428835520063351784044953670659899444567206859375}{4201311152064506613538821375147148793359302023089508811528133782221774152384}\cdot t^{45}-\frac{939891648062995415464978327275157125977104222479598436060323463676173614082086039068420767822338995868125}{8402622304129013227077642750294297586718604046179017623056267564443548304768}\cdot t^{43}+\frac{53106121095297088781844619809815064205349813596636810131738705202195494403776449718628540027313118690860625}{16805244608258026454155285500588595173437208092358035246112535128887096609536}\cdot t^{41}-\frac{2529202515581389526946924368881935509239268831365625229938669803730249456643114766889781110253254892770154375}{33610489216516052908310571001177190346874416184716070492225070257774193219072}\cdot t^{39}+\frac{101444642069876696500860115026179356434408033451710372568617217347885983684125150988027837912895487549197320625}{67220978433032105816621142002354380693748832369432140984450140515548386438144}\cdot t^{37}-\frac{3420097997518874707639787722839548756855971448957407315574794790582122497595149183822291566501845565938582846875}{134441956866064211633242284004708761387497664738864281968900281031096772876288}\cdot t^{35}+\frac{96626018954097983118276613222265938937599946097415267008066724242761046330896423730345334730312106223525806534375}{268883913732128423266484568009417522774995329477728563937800562062193545752576}\cdot t^{33}-\frac{2278174246088224527201219338362110230315686846576604290571385063466636563981738776879255171755104983907269999540625}{537767827464256846532969136018835045549990658955457127875601124124387091505152}\cdot t^{31}+\frac{44584527614373114366877188303757184957410983478076664313793260799546712550741206518748693772911298826244155156615625}{1075535654928513693065938272037670091099981317910914255751202248248774183010304}\cdot t^{29}-\frac{719409337003033774067145771957330278558107573156143978796823881284562009856916794908205998564688644899571211711446875}{2151071309857027386131876544075340182199962635821828511502404496497548366020608}\cdot t^{27}+\frac{30523879176567723346739748730347552895814220743441305650054782594280407189420997902766802411628611691960296245890625}{13833256011942298303098884527815692490031914056732016151140864929244684025856}\cdot t^{25}-\frac{101422575030245193720812292288608614008077339166032582712709965119737770423788280010920067648248641907015529341035390625}{8604285239428109544527506176301360728799850543287314046009617985990193464082432}\cdot t^{23}+\frac{866863268804497038558526027673211427104928065267157795956503903032703868680180057401149186499082419740098963445591328125}{17208570478856219089055012352602721457599701086574628092019235971980386928164864}\cdot t^{21}-\frac{5841196239114460459139180694876414571868354038319884363708967328524880782760880727359211727380087705425518781087646109375}{34417140957712438178110024705205442915199402173149256184038471943960773856329728}\cdot t^{19}+\frac{30480238741602310353245213980481469252806540533120891724791707888274701674303119955023568862728191262879678058241773421875}{68834281915424876356220049410410885830398804346298512368076943887921547712659456}\cdot t^{17}-\frac{120459071311990455976978370347748517123604276204462703990037751191294913371955111632843740693006844901873163174795785078125}{137668563830849752712440098820821771660797608692597024736153887775843095425318912}\cdot t^{15}+\frac{350479058458077646360280268004239593907587981682382343575249399023603857552150016003050451708636982005939225717866704453125}{275337127661699505424880197641643543321595217385194049472307775551686190850637824}\cdot t^{13}-\frac{723200397006924227271616222366980712955545073216460509427383824004642908187231152786406214122970674484940094943909294609375}{550674255323399010849760395283287086643190434770388098944615551103372381701275648}\cdot t^{11}+\frac{1004958001255176144643546006817791363900277499432691879900111677657501314926983091276058853497493897104862383995597000546875}{1101348510646798021699520790566574173286380869540776197889231102206744763402551296}\cdot t^9-\frac{871049670861909783381013644036381337864238468842662423328862479393224322114792580681311787233698421758056046854991415078125}{2202697021293596043399041581133148346572761739081552395778462204413489526805102592}\cdot t^7+\frac{25996047268441670871094186631159584923432550914816678633781650024782478171336325635779169452132228359227253121479480078125}{275337127661699505424880197641643543321595217385194049472307775551686190850637824}\cdot t^5-\frac{10873132031107224033992067893501040070534885904924542030584688318262183740878364494745350281193833573612758307800273828125}{1101348510646798021699520790566574173286380869540776197889231102206744763402551296}\cdot t^3+\frac{1157836495791911396137300524888798179947835184975171255160835578936430546658569009717187050033322783547062553437336328125}{4405394042587192086798083162266296693145523478163104791556924408826979053610205184}\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.