Rule: Q[8, 40]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{48}-\frac{911482131494893539006537177845526565971616}{947397510533097832003392609306155659087}\cdot t^{46}+\frac{6798195690026501725016335724232682059442211100}{16105757679062663144057674358204646204479}\cdot t^{44}-\frac{19862645329230318955479624296418311683910550339840}{177163334469689294584634417940251108249269}\cdot t^{42}+\frac{3576463550867792036434055918950525505242656874689555}{177163334469689294584634417940251108249269}\cdot t^{40}-\frac{27250536266687872250243013799204190125069333016581740}{10421372615864076152037318702367712249957}\cdot t^{38}+\frac{44709993956122182236766831522211726233937228845550509390}{177163334469689294584634417940251108249269}\cdot t^{36}-\frac{3286182825639792546419050096576158760824053237028678340500}{177163334469689294584634417940251108249269}\cdot t^{34}+\frac{997124310869871746738357969768965794161172876188818066200}{947397510533097832003392609306155659087}\cdot t^{32}-\frac{44023601516343704440726545390955358662824649228902280400400}{947397510533097832003392609306155659087}\cdot t^{30}+\frac{1517770976182710018100586571154554838360170824452562787458400}{947397510533097832003392609306155659087}\cdot t^{28}-\frac{40860958444742597978569404054661946163448720763623465960393200}{947397510533097832003392609306155659087}\cdot t^{26}+\frac{856242228681188608156353816777796222371505551102842780759906250}{947397510533097832003392609306155659087}\cdot t^{24}-\frac{13877620190364431128585182918001589864443278197851344339422355000}{947397510533097832003392609306155659087}\cdot t^{22}+\frac{172294862513073155256711022112742900203620941295457978538099547500}{947397510533097832003392609306155659087}\cdot t^{20}-\frac{1616759897796846080743667748697187215233621802189291674056386485000}{947397510533097832003392609306155659087}\cdot t^{18}+\frac{11262269130152386726031375567264209134435722638830546359945960664375}{947397510533097832003392609306155659087}\cdot t^{16}-\frac{56863105452286156000766359758728494699802735575565771190245634750000}{947397510533097832003392609306155659087}\cdot t^{14}+\frac{201528319728119226257854161033223093965144600334859748934203949012500}{947397510533097832003392609306155659087}\cdot t^{12}-\frac{479812904312580375532562353664550829840995006671830482535142385150000}{947397510533097832003392609306155659087}\cdot t^{10}+\frac{721238334279968779743512967357714511872101366322596950294966294978125}{947397510533097832003392609306155659087}\cdot t^8-\frac{624610483741772547519781907577192611871477260160925056851171091262500}{947397510533097832003392609306155659087}\cdot t^6+\frac{270020529531609689990719298095787857604109977134098572526612057656250}{947397510533097832003392609306155659087}\cdot t^4-\frac{45089021412810599911814209738234209597934675837293212298214401937500}{947397510533097832003392609306155659087}\cdot t^2+\frac{1367263188133790621263854499799567347125076268446172813975392781250}{947397510533097832003392609306155659087}$

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.