Rule: Q[8, 54]

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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{62}-\frac{27821523064529912692435739254262507415791646844411979987405951493208192}{128651022320933044139814050041098820260134650050172833883069711283}\cdot t^{60}+\frac{10971054632015224571667441014053265681931077124430343723243721195148613760}{128651022320933044139814050041098820260134650050172833883069711283}\cdot t^{58}-\frac{126264731659353187834577761585484759035290662617056603376121994960447514677120}{6046598049083853074571260351931644552226328552358123192504276430301}\cdot t^{56}+\frac{495551700460590171259335390075768006561499357916309133006550894917703483722252240}{139071755128928620715138988094427824701205556704236833427598357896923}\cdot t^{54}-\frac{62688528258234849252191444866253152556053598199832713491468448314646480475800845400}{139071755128928620715138988094427824701205556704236833427598357896923}\cdot t^{52}+\frac{469740987722443042562038132380886526987462306726759316624117721620873511126150636800}{10697827317609893901164537545725217284708119746479756417507565992071}\cdot t^{50}-\frac{36132312981476066532479275186190946225139346312172860864741248986007834565509815604500}{10697827317609893901164537545725217284708119746479756417507565992071}\cdot t^{48}+\frac{47510117192017816202489784329422219833326856488714420268945019551684677097648987461625}{227613347183189231939671011611174835844853611627228859946969489193}\cdot t^{46}-\frac{207646533664692037985182965925831426494343021408030772884032228005828547302243858800125}{19792464972451237559971392314015203116943792315411205212779955582}\cdot t^{44}+\frac{8561163447713139347776178791273768675187089569705630444640169527535348033848862806677375}{19792464972451237559971392314015203116943792315411205212779955582}\cdot t^{42}-\frac{145622449868847300452542808590056405307117386890089969442223810272444351922248048613939750}{9896232486225618779985696157007601558471896157705602606389977791}\cdot t^{40}+\frac{65645812970220694529720329535799273031430146036049989618665397963998532464624489736068830625}{158339719779609900479771138512121624935550338523289641702239644656}\cdot t^{38}-\frac{3069521616610752263809841717743576174639468893974529067410303406417734882234582683104551039375}{316679439559219800959542277024243249871100677046579283404479289312}\cdot t^{36}+\frac{29785999235022868124130534124817207738367826830604017462442065854456125061995170547005362311875}{158339719779609900479771138512121624935550338523289641702239644656}\cdot t^{34}-\frac{1917414549401239020330081382082389508646921337515070829268157384913421199870667669178691808754375}{633358879118439601919084554048486499742201354093158566808958578624}\cdot t^{32}+\frac{102097097934195139183591073831271253662991363224199921422847792289839722388456105509317014013023125}{2533435516473758407676338216193945998968805416372634267235834314496}\cdot t^{30}-\frac{2239568736258893179473295850093611397654462311922945465041844530958013470876157971583169246613784375}{5066871032947516815352676432387891997937610832745268534471668628992}\cdot t^{28}+\frac{20126909555686204283871454935614617015580736844977046672886475757826787117511704270562014181652221875}{5066871032947516815352676432387891997937610832745268534471668628992}\cdot t^{26}-\frac{147135949576739816531304405350498824632745868591175252723612509760504276079629989544068681910271265625}{5066871032947516815352676432387891997937610832745268534471668628992}\cdot t^{24}+\frac{6934424032572255809631750698117930572909268481867333069268273947664582795638464976211143152064103171875}{40534968263580134522821411459103135983500886661962148275773349031936}\cdot t^{22}-\frac{65062211031221197641682211049459672726634608902446192953748873061792566792695904020387003315024265453125}{81069936527160269045642822918206271967001773323924296551546698063872}\cdot t^{20}+\frac{59852546422244988588671107992886692705268546881819977321549034080023476537002996453579027024709851953125}{20267484131790067261410705729551567991750443330981074137886674515968}\cdot t^{18}-\frac{1355655997725256677316989268826276413279706777011381663723454855156179810163027687543165823153967285546875}{162139873054320538091285645836412543934003546647848593103093396127744}\cdot t^{16}+\frac{11523200647363883831740943317286412153088780279599966820656992646707087072651876861849328104966076816328125}{648559492217282152365142583345650175736014186591394372412373584510976}\cdot t^{14}-\frac{35580745727882271718734286757843723690876420476319880146157621959682260914055976066608949712799909345484375}{1297118984434564304730285166691300351472028373182788744824747169021952}\cdot t^{12}+\frac{38196531112873247811261224452083809605956634668964227929617181535806694428503987446541419115168477055765625}{1297118984434564304730285166691300351472028373182788744824747169021952}\cdot t^{10}-\frac{13405939065491022162910554882191053679608227136044839888142489981655252651604315915754959164237979106796875}{648559492217282152365142583345650175736014186591394372412373584510976}\cdot t^8+\frac{89843674993350492632313634505403994482656789015279847898721680777329624315524813672548207878504525428671875}{10376951875476514437842281333530402811776226985462309958597977352175616}\cdot t^6-\frac{38663080496159861154478027386840729783237464272374073602852077881140616277395141614981375867209659731328125}{20753903750953028875684562667060805623552453970924619917195954704351232}\cdot t^4+\frac{1595859287606451215642036817876142523570850015220038188755428531743414322825199552021355768896715232421875}{10376951875476514437842281333530402811776226985462309958597977352175616}\cdot t^2-\frac{84372965019351699469082569383443729271191791909111685313376792093631767913216852755690697141377981640625}{41507807501906057751369125334121611247104907941849239834391909408702464}$

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.