Rule: Q[2, 3, 58]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{63}-\frac{492244951036495519031005917339353859656122845227156862587749829183341559}{134094278364037108667269878114219623605730279713457992112198785595916}\cdot t^{61}+\frac{181056842712111241122917634668850787980397081671034324323079923626348894041}{114937952883460378857659895526473963090625954040106850381884673367928}\cdot t^{59}-\frac{84574113680665078028708531242201599606496722533051707549613485769486131097849}{201141417546055663000904817171329435408595419570186988168298178393874}\cdot t^{57}+\frac{6003072704453338127610171674452281267968812830169508767328666757942893417233963}{76625301922306919238439930350982642060417302693404566921256448911952}\cdot t^{55}-\frac{1107472062282512187273022728265579892088829115266686192389267062426430288919197505}{102167069229742558984586573801310189413889736924539422561675265215936}\cdot t^{53}+\frac{236387233084824448615367192580653971588805105496929556032139027102727600040747872935}{204334138459485117969173147602620378827779473849078845123350530431872}\cdot t^{51}-\frac{19953492860197876586297548391503644254175211404052993365199123642500787110576611316825}{204334138459485117969173147602620378827779473849078845123350530431872}\cdot t^{49}+\frac{1355345461137853142521937106439230258557726364642797157459547344828627048665885621342475}{204334138459485117969173147602620378827779473849078845123350530431872}\cdot t^{47}-\frac{599886896616351319091567841741532803949363553666406987456354453593773794764542233208617075}{1634673107675880943753385180820963030622235790792630760986804243454976}\cdot t^{45}+\frac{54525946932954008600828658894679329863802732024157541649360880083559562919205238821858454625}{3269346215351761887506770361641926061244471581585261521973608486909952}\cdot t^{43}-\frac{1023613792447317668308931387008702278121538328400046308292477352972938405811991904027796928875}{1634673107675880943753385180820963030622235790792630760986804243454976}\cdot t^{41}+\frac{127455082545295814650642640605518058455467514242548775059779418704052423601097770969819746146375}{6538692430703523775013540723283852122488943163170523043947216973819904}\cdot t^{39}-\frac{13180278904538253952006288843253405949370916768295929632309383083984827902648834068842600065554625}{26154769722814095100054162893135408489955772652682092175788867895279616}\cdot t^{37}+\frac{566057250861111891201642010372207367910807198229448594303366896632021345891570309581091459205221375}{52309539445628190200108325786270816979911545305364184351577735790559232}\cdot t^{35}-\frac{10082568210430102243352370827206489700410278746404866233453436026775389332211383735958804412916254375}{52309539445628190200108325786270816979911545305364184351577735790559232}\cdot t^{33}+\frac{2321057926554982262813690865677576049878014384451854369249984860353119065576183282405447898986976875}{817336553837940471876692590410481515311117895396315380493402121727488}\cdot t^{31}-\frac{14420277019847743743920233351369499644261871308720124462120095165915158694463232184133710955021165525625}{418476315565025521600866606290166535839292362442913474812621886324473856}\cdot t^{29}+\frac{286551004907065092338270252092648663016951699887440708268170006498059437901300678367689978613116155006875}{836952631130051043201733212580333071678584724885826949625243772648947712}\cdot t^{27}-\frac{36149734832924952976677284302345992391265221132335531931458600843211453571192065655486701435645321213125}{13077384861407047550027081446567704244977886326341046087894433947639808}\cdot t^{25}+\frac{30069311976321908647206070365453808031621900743887710736372524344012298103715699698568427299641915716484375}{1673905262260102086403466425160666143357169449771653899250487545297895424}\cdot t^{23}-\frac{621635346825401945171066403345459477517638197365681092268388612873688550682450068902943941462088675536796875}{6695621049040408345613865700642664573428677799086615597001950181191581696}\cdot t^{21}+\frac{5035412028356950171485966463051207161631888600936214502781963910195502662861900005121734436651922606219328125}{13391242098080816691227731401285329146857355598173231194003900362383163392}\cdot t^{19}-\frac{15690372647399488891495215725298553804983693266420527075175325928343929392549509739202629885010819674957984375}{13391242098080816691227731401285329146857355598173231194003900362383163392}\cdot t^{17}+\frac{36758402613548150911526924198037038500987081103343147705579538632535902740673704123886710982316950550794984375}{13391242098080816691227731401285329146857355598173231194003900362383163392}\cdot t^{15}-\frac{503043489544054392579509144066076861724575759950174064261912931543324934670204724948556199419924676558302765625}{107129936784646533529821851210282633174858844785385849552031202899065307136}\cdot t^{13}+\frac{1210106144776656129098228163424125017523606575170933911608626685218009034898048451763470641832544215328523421875}{214259873569293067059643702420565266349717689570771699104062405798130614272}\cdot t^{11}-\frac{486622950079600104639844949344733815393206227280880917089286879966807134199760773359734259560089514441205484375}{107129936784646533529821851210282633174858844785385849552031202899065307136}\cdot t^9+\frac{976202326485979699469550604609900249537112693513810531540980470307681784360197039145071835699685209092004015625}{428519747138586134119287404841130532699435379141543398208124811596261228544}\cdot t^7-\frac{1099706733591692942422626261430363835106060116487450861231346821948720354070862110714346086257974672748645421875}{1714078988554344536477149619364522130797741516566173592832499246385044914176}\cdot t^5+\frac{289980129814260404123084633250867520402497739057508471248351922841217660555797014054256991250265836128618828125}{3428157977108689072954299238729044261595483033132347185664998492770089828352}\cdot t^3-\frac{11685665056427044973903075599360722831692665676964142599229064574494868489447326295943260462326120957898515625}{3428157977108689072954299238729044261595483033132347185664998492770089828352}\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.