Rule: Q[3, 80]

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^{83}-\frac{35364480383805091167994390542705365237556838988}{2536715008713235491535654685913474885538809}\cdot t^{81}+\frac{9773782938631517622805471365204257789953040664360}{845571669571078497178551561971158295179603}\cdot t^{79}-\frac{394966668858608594894972062713183645147746524677420}{65043974582390653629119350920858330398431}\cdot t^{77}+\frac{147715054432795323129298568377667273601901260193440765}{65043974582390653629119350920858330398431}\cdot t^{75}-\frac{83788932600457776735047413173983134090012897087293916575}{130087949164781307258238701841716660796862}\cdot t^{73}+\frac{18745526187966398660200172476741043961482560254022977677925}{130087949164781307258238701841716660796862}\cdot t^{71}-\frac{6795153028433553196475861321274822452824565096304648607203375}{260175898329562614516477403683433321593724}\cdot t^{69}+\frac{8135510717143087900845115837808611653105669387751727382745978875}{2081407186636500916131819229467466572749792}\cdot t^{67}-\frac{2039108736278358797979707385608829430462822442408527045530549323625}{4162814373273001832263638458934933145499584}\cdot t^{65}+\frac{27034717749588020354806707078481462442564910701271936499097874547125}{520351796659125229032954807366866643187448}\cdot t^{63}-\frac{4893334165865414180360746094120547444603449291714371891500107382141375}{1040703593318250458065909614733733286374896}\cdot t^{61}+\frac{1520967009513507364143151738149564820676247019502753394293689553823219375}{4162814373273001832263638458934933145499584}\cdot t^{59}-\frac{203933708109809729461977545769271733050044943893139890141093624251974573125}{8325628746546003664527276917869866290999168}\cdot t^{57}+\frac{11838031221685706643066274097196007701082635675276022069524622309669938568125}{8325628746546003664527276917869866290999168}\cdot t^{55}-\frac{1193132267030113611973182980468809135212958245315663969699683895660755320344375}{16651257493092007329054553835739732581998336}\cdot t^{53}+\frac{836652316305092821468852524642182107024908799998732208861820395855624651764174375}{266420119889472117264872861371835721311973376}\cdot t^{51}-\frac{63842737546982802321613648180601603991606702673122895695041894070074166585830578125}{532840239778944234529745722743671442623946752}\cdot t^{49}+\frac{1060630339061032836206701497879645982620305673990234303515638554699282576726018609375}{266420119889472117264872861371835721311973376}\cdot t^{47}-\frac{61360744105679419639703729557352587393752406449263386500557150504943653732633277328125}{532840239778944234529745722743671442623946752}\cdot t^{45}+\frac{6175343214189121241397918052272557913750213691440419741429256721801868592817084407984375}{2131360959115776938118982890974685770495787008}\cdot t^{43}-\frac{269866828762387137354002175769790016047314383209361861430044288375415565042449397500828125}{4262721918231553876237965781949371540991574016}\cdot t^{41}+\frac{5109977214500147506565294948621028051790069402344642105965387293748810001974695810814296875}{4262721918231553876237965781949371540991574016}\cdot t^{39}-\frac{167228173626999946846908054316640501630887035634799375695323581174014226262522590436882890625}{8525443836463107752475931563898743081983148032}\cdot t^{37}+\frac{18850709507374352001643932631379922740848878501697237149676658051147098601044332245019013359375}{68203550691704862019807452511189944655865184256}\cdot t^{35}-\frac{455510383463210695698089495359983445255929245940775497612703086489091110469378035446747815453125}{136407101383409724039614905022379889311730368512}\cdot t^{33}+\frac{1173718312421545373383289385005624312786817004373705598852488959608390926901440907249801748265625}{34101775345852431009903726255594972327932592128}\cdot t^{31}-\frac{20514095620893206378110499596635475709801661834521084556295335212223200045828531665868256149296875}{68203550691704862019807452511189944655865184256}\cdot t^{29}+\frac{603610455530156364001755000427048559393302782551133274616025234148977023055612961277263427942109375}{272814202766819448079229810044759778623460737024}\cdot t^{27}-\frac{7411088291624062751946387410539157980828532328872601347652396456805583342019023275509170588678203125}{545628405533638896158459620089519557246921474048}\cdot t^{25}+\frac{37582043279846682042805942182996054920863034206752258409243816777316017024928138029519384644078515625}{545628405533638896158459620089519557246921474048}\cdot t^{23}-\frac{311015716474128442982181505492386094974471029438477485493454508756865860869663658045732510813735546875}{1091256811067277792316919240179039114493842948096}\cdot t^{21}+\frac{33107914016691905011189088602069138042292899933616602771639576107025701999815949262049554591208794921875}{34920217954152889354141415685729251663802974339072}\cdot t^{19}-\frac{173897557709565312729745435478540996218107407385727724117144221935553440970371020224540013288872306640625}{69840435908305778708282831371458503327605948678144}\cdot t^{17}+\frac{176235924605363481310601957291814640762515242388169415690337913134700971578059394273005061877844494140625}{34920217954152889354141415685729251663802974339072}\cdot t^{15}-\frac{535722874503484949674375437315264855920769232171833321790594813001545506557243304964410331400450044921875}{69840435908305778708282831371458503327605948678144}\cdot t^{13}+\frac{2351864559160477640140095011938705088067301861109686384877428841928948426314669850809157067725255298828125}{279361743633223114833131325485834013310423794712576}\cdot t^{11}-\frac{3541202245522215155216692939273498261971708226696717855218704743607639130589298087544760769351463662109375}{558723487266446229666262650971668026620847589425152}\cdot t^9+\frac{1698816129065944326465107349426018241649848161779117113885249050480594864789062518000395339778198330078125}{558723487266446229666262650971668026620847589425152}\cdot t^7-\frac{926272667464136178384886233899151667103813735835432904512946755386870319055728138756215513813192490234375}{1117446974532892459332525301943336053241695178850304}\cdot t^5+\frac{937798188508148488673176202722755050242324615328264286164605560514958787840422613973756613899662802734375}{8939575796263139674660202415546688425933561430802432}\cdot t^3-\frac{69462710455036156021570695479001836588841621572275292767043734071442482192081738233509588828253642578125}{17879151592526279349320404831093376851867122861604864}\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.