Rule: Q[2, 10, 27]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{12}-\frac{8477}{76}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{152}\cdot t^6+\frac{1500975}{304}\cdot t^4-\frac{2132865}{1216}\cdot t^2+\frac{110565}{2432}$
• $P_3$:
  $4\cdot t^{39}-\frac{1699639380422035860256037577242097457139069086751030885127668113}{1500637075048149269098881991624565516591054469337454092471740}\cdot t^{37}+\frac{429038355398161828889365226829014092834850702404758995488208614483}{3001274150096298538197763983249131033182108938674908184943480}\cdot t^{35}-\frac{266524801894579297858460138076877852304268658000950525920206403552}{25010617917469154484981366527076091943184241155624234874529}\cdot t^{33}+\frac{11955739752686559052290081116677820992027048285126439151931313433975637}{22809683540731868890303006272693395852184027933929302205570448}\cdot t^{31}-\frac{6980141574796706827799742155234405169264882622136575795065168664339109935}{387764620192441771135151106635787729487128474876798137494697616}\cdot t^{29}+\frac{115176643142478710710959655623903327755254378329666384904492026276213686823}{258509746794961180756767404423858486324752316584532091663131744}\cdot t^{27}-\frac{8363250599208407524714214059977106889245227514701700379796747864060268710441}{1034038987179844723027069617695433945299009266338128366652526976}\cdot t^{25}+\frac{224490439976626866576254251492728378039515044964962910461158640589651579645025}{2068077974359689446054139235390867890598018532676256733305053952}\cdot t^{23}-\frac{4457950272987217811258900752797397368931558409773362882313239946493232410148525}{4136155948719378892108278470781735781196037065352513466610107904}\cdot t^{21}+\frac{65100226833919698386864763466479028260636450459354111720081347429947781014318875}{8272311897438757784216556941563471562392074130705026933220215808}\cdot t^{19}-\frac{36328817951232693326533790555835867144409653611257517008108782735771584452238025}{870769673414606082549111257006681217093902540074213361391601664}\cdot t^{17}+\frac{16118831651746527488539500069580430975484992231105622715199678977381473939699075}{102443490989953656770483677294903672599282651773436866046070784}\cdot t^{15}-\frac{41967068385153612784794529032567349060705185663024948511005616076786351464027125}{102443490989953656770483677294903672599282651773436866046070784}\cdot t^{13}+\frac{144491275364217657236794189962572293766728030337639753528702270453908978451590875}{204886981979907313540967354589807345198565303546873732092141568}\cdot t^{11}-\frac{617701484603890637377782810605947576933461268949791875174171242766079622363353125}{819547927919629254163869418359229380794261214187494928368566272}\cdot t^9+\frac{744438523489061730674210229680924396640027797758851058299742535680153277155724625}{1639095855839258508327738836718458761588522428374989856737132544}\cdot t^7-\frac{861997151104789622846530095616976968546854726133670627466957836366972677372729875}{6556383423357034033310955346873835046354089713499959426948530176}\cdot t^5+\frac{177595302715239927795297542804004741059911257736318979116767128220130502678180625}{13112766846714068066621910693747670092708179426999918853897060352}\cdot t^3-\frac{3754787818672758098787787105763695113486284272662569056150835774027216450529375}{13112766846714068066621910693747670092708179426999918853897060352}\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.