Rule: Q[1, 20, 36]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{21}-210\cdot t^{19}+17955\cdot t^{17}-813960\cdot t^{15}+21366450\cdot t^{13}-333316620\cdot t^{11}+3055402350\cdot t^9-15713497800\cdot t^7+41247931725\cdot t^5-45831035250\cdot t^3+13749310575\cdot t$
• $P_3$:
  $t^{57}-\frac{411287889662130948830614956}{343303287907604831431525}\cdot t^{55}+\frac{456602185512307029270930226443}{686606575815209662863050}\cdot t^{53}-\frac{359183344222952161495206411922161}{1579195124374982224585015}\cdot t^{51}+\frac{1868078708065313720227478277168698187}{34742292736249608940870330}\cdot t^{49}-\frac{32459987023876327598438383631644412940}{3474229273624960894087033}\cdot t^{47}+\frac{21519984755444280436122050814165857761137}{17371146368124804470435165}\cdot t^{45}-\frac{2231418723268570049243015714812442190977718}{17371146368124804470435165}\cdot t^{43}+\frac{36794039193304667069530838349107173172420952}{3474229273624960894087033}\cdot t^{41}-\frac{2439445842043945035992360410868603998812403848}{3474229273624960894087033}\cdot t^{39}+\frac{262092661436349985122502190520982956603125770869}{6948458547249921788174066}\cdot t^{37}-\frac{5730417550047815127907866494260172246061470177649}{3474229273624960894087033}\cdot t^{35}+\frac{408864614088280072764891076945267146007627719727497}{6948458547249921788174066}\cdot t^{33}-\frac{541001649252312406657964355283768669589897827341480}{315839024874996444917003}\cdot t^{31}+\frac{12828267099018162532921111994262392746478375371854570}{315839024874996444917003}\cdot t^{29}-\frac{246891092009644708430049202749939136835142937098944940}{315839024874996444917003}\cdot t^{27}+\frac{3835438843651576555253050390252851716824483050217829175}{315839024874996444917003}\cdot t^{25}-\frac{2075210789906061433463733256939398546791295029724042300}{13732131516304193257261}\cdot t^{23}+\frac{40962236383265312658053651905993701356725724914310677125}{27464263032608386514522}\cdot t^{21}-\frac{158258156591001580942901529339480693717945331526737981125}{13732131516304193257261}\cdot t^{19}+\frac{1883554064605383073125954233400323381683561353087006199125}{27464263032608386514522}\cdot t^{17}-\frac{4225935961086012916046843408472497994692689332411412555500}{13732131516304193257261}\cdot t^{15}+\frac{13911046884005759060345008389438453321085391957338317647625}{13732131516304193257261}\cdot t^{13}-\frac{32389028069824624358032245584122335988196147142514421193750}{13732131516304193257261}\cdot t^{11}+\frac{50727844873917410161171356469117061273534026064746437506250}{13732131516304193257261}\cdot t^9-\frac{49721606966365901323370667920059386801967385386129379610000}{13732131516304193257261}\cdot t^7+\frac{54584908442380668654488506443791846519411910125964612309375}{27464263032608386514522}\cdot t^5-\frac{6931255637463360129590431469199120113045897370906599596875}{13732131516304193257261}\cdot t^3+\frac{1067583015073643668378398532684940793829042330432387321875}{27464263032608386514522}\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.