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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{12}-\frac{8477}{152}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{76}\cdot t^6+\frac{1500975}{76}\cdot t^4-\frac{2132865}{152}\cdot t^2+\frac{110565}{152}$
• $P_3$:
  $t^{39}-\frac{1699639380422035860256037577242097457139069086751030885127668113}{3001274150096298538197763983249131033182108938674908184943480}\cdot t^{37}+\frac{429038355398161828889365226829014092834850702404758995488208614483}{3001274150096298538197763983249131033182108938674908184943480}\cdot t^{35}-\frac{533049603789158595716920276153755704608537316001901051840412807104}{25010617917469154484981366527076091943184241155624234874529}\cdot t^{33}+\frac{11955739752686559052290081116677820992027048285126439151931313433975637}{5702420885182967222575751568173348963046006983482325551392612}\cdot t^{31}-\frac{6980141574796706827799742155234405169264882622136575795065168664339109935}{48470577524055221391893888329473466185891059359599767186837202}\cdot t^{29}+\frac{115176643142478710710959655623903327755254378329666384904492026276213686823}{16156859174685073797297962776491155395297019786533255728945734}\cdot t^{27}-\frac{8363250599208407524714214059977106889245227514701700379796747864060268710441}{32313718349370147594595925552982310790594039573066511457891468}\cdot t^{25}+\frac{224490439976626866576254251492728378039515044964962910461158640589651579645025}{32313718349370147594595925552982310790594039573066511457891468}\cdot t^{23}-\frac{4457950272987217811258900752797397368931558409773362882313239946493232410148525}{32313718349370147594595925552982310790594039573066511457891468}\cdot t^{21}+\frac{65100226833919698386864763466479028260636450459354111720081347429947781014318875}{32313718349370147594595925552982310790594039573066511457891468}\cdot t^{19}-\frac{36328817951232693326533790555835867144409653611257517008108782735771584452238025}{1700722018387902504978732923841174252136528398582447971467972}\cdot t^{17}+\frac{16118831651746527488539500069580430975484992231105622715199678977381473939699075}{100042471669876617939925466108304367772736964622496939498116}\cdot t^{15}-\frac{41967068385153612784794529032567349060705185663024948511005616076786351464027125}{50021235834938308969962733054152183886368482311248469749058}\cdot t^{13}+\frac{144491275364217657236794189962572293766728030337639753528702270453908978451590875}{50021235834938308969962733054152183886368482311248469749058}\cdot t^{11}-\frac{617701484603890637377782810605947576933461268949791875174171242766079622363353125}{100042471669876617939925466108304367772736964622496939498116}\cdot t^9+\frac{744438523489061730674210229680924396640027797758851058299742535680153277155724625}{100042471669876617939925466108304367772736964622496939498116}\cdot t^7-\frac{861997151104789622846530095616976968546854726133670627466957836366972677372729875}{200084943339753235879850932216608735545473929244993878996232}\cdot t^5+\frac{177595302715239927795297542804004741059911257736318979116767128220130502678180625}{200084943339753235879850932216608735545473929244993878996232}\cdot t^3-\frac{3754787818672758098787787105763695113486284272662569056150835774027216450529375}{100042471669876617939925466108304367772736964622496939498116}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.