Rule: Q[2, 3, 56]

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^{61}-\frac{531599802575561949837609695594068504860910779049284228655925262175154}{155305158738556770794039759038947868295261702838393123027590315211}\cdot t^{59}+\frac{212179687376320765652573318733372064975260704791327559930903425099918696}{155305158738556770794039759038947868295261702838393123027590315211}\cdot t^{57}-\frac{17512015686543560271780997712410320886841157386735082574677947147616172015}{51768386246185590264679919679649289431753900946131041009196771737}\cdot t^{55}+\frac{1341311773706832769894895112646708357221462581247143304776505661217299623395}{23008171664971373450968853190955239747446178198280462670754120772}\cdot t^{53}-\frac{342241692772272476496952590768018421937418310177734806294397765457804109305565}{46016343329942746901937706381910479494892356396560925341508241544}\cdot t^{51}+\frac{33564290476100833931882072803950715344476063035152827618158283122269152129868675}{46016343329942746901937706381910479494892356396560925341508241544}\cdot t^{49}-\frac{2593944685139722361721947084212374966941940784820698922301301446745149712723786575}{46016343329942746901937706381910479494892356396560925341508241544}\cdot t^{47}+\frac{1285384650236233089409638250858221941421933615931498304461631965597710479816673785625}{368130746639541975215501651055283835959138851172487402732065932352}\cdot t^{45}-\frac{129135441594562647295929616746619721278328068704271431943225376833444874779556890864875}{736261493279083950431003302110567671918277702344974805464131864704}\cdot t^{43}+\frac{2651487285725600837627607299692222179330677990047296558345839945262467676968810797549125}{368130746639541975215501651055283835959138851172487402732065932352}\cdot t^{41}-\frac{380363311074296569628988056982229920079546203942370803055604596660525169951091035131125}{1564849082421007333540920939661142767095170461944686090253202688}\cdot t^{39}+\frac{39824100866926819643654094713136725823738904725641442188607861980473020568170420156246499875}{5890091946232671603448026416884541375346221618759798443713054917632}\cdot t^{37}-\frac{1828085976689548484175854532117484695669825028039610974042338305161496473584310908214683733125}{11780183892465343206896052833769082750692443237519596887426109835264}\cdot t^{35}+\frac{34598648067095023794966659507210776752299331205969857052218636112604179121059203773288229598125}{11780183892465343206896052833769082750692443237519596887426109835264}\cdot t^{33}-\frac{269369089138379618722924515685030523339168247133600661514174077005771647699863057575544886140625}{5890091946232671603448026416884541375346221618759798443713054917632}\cdot t^{31}+\frac{54999045889710372226490209055186983179441375090035664943544193915020235755854967410403316816736875}{94241471139722745655168422670152662005539545900156775099408878682112}\cdot t^{29}-\frac{1143989351046907472336554147515540938250013767293232561591424115475811305430035617642384394747335625}{188482942279445491310336845340305324011079091800313550198817757364224}\cdot t^{27}+\frac{1203100832681531766984073925614648244417065927312938514997599787296930552070280406315483506041071875}{23560367784930686413792105667538165501384886475039193774852219670528}\cdot t^{25}-\frac{129780332582422967896636629421329496990553160233150342922636003166632907299511842165439467302505515625}{376965884558890982620673690680610648022158183600627100397635514728448}\cdot t^{23}+\frac{2771444309825952923763506594739671667890032993000982751365261369373219599031050503522754289936381890625}{1507863538235563930482694762722442592088632734402508401590542058913792}\cdot t^{21}-\frac{23088626633363033443185874407886030979294427018563965226179356301232539289395409150259419587497077859375}{3015727076471127860965389525444885184177265468805016803181084117827584}\cdot t^{19}+\frac{73673697318669602671812619065590824191010754036251271190641371878311717748394014513971827611833135578125}{3015727076471127860965389525444885184177265468805016803181084117827584}\cdot t^{17}-\frac{176022727273423024629757482929225251777726059822095179432716285373762898136013610700975692280008544609375}{3015727076471127860965389525444885184177265468805016803181084117827584}\cdot t^{15}+\frac{2448347587789908879688322577537015224311501253301530126985678617589552938782354886041929981650084399296875}{24125816611769022887723116203559081473418123750440134425448672942620672}\cdot t^{13}-\frac{5976867364098877453437375450927436347772154766208075931272819338580885212160216521727194126571306273640625}{48251633223538045775446232407118162946836247500880268850897345885241344}\cdot t^{11}+\frac{2445865643116913764584425074263797990339962008369775414656104264501482598305079843131071925458343710140625}{24125816611769022887723116203559081473418123750440134425448672942620672}\cdot t^9-\frac{5052907990792581499684354565964866361423492955219999243677738216332917819482084190171861402817748341859375}{96503266447076091550892464814236325893672495001760537701794691770482688}\cdot t^7+\frac{6031071511372815417376327340330515016459578511185159936830611708016826956808878764931116167234429364765625}{386013065788304366203569859256945303574689980007042150807178767081930752}\cdot t^5-\frac{1771927982075684331685202334898220132528574230532615473298769037433890026199164417773882720985101860859375}{772026131576608732407139718513890607149379960014084301614357534163861504}\cdot t^3+\frac{84515877519463442811358795544314993892329305257039201253863152174547225633262421122365918536098631171875}{772026131576608732407139718513890607149379960014084301614357534163861504}\cdot t$

Warning: This rule has negative weights!

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.