Rule: Q[8, 50]

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^{58}-\frac{17392010149223995452877145897730707518500457601339737431671}{11998724209199654391509790114482532688358698626274742307}\cdot t^{56}+\frac{128655825981263233338502526515785021565985161817053035849549970}{131985966301196198306607691259307859571945684889022165377}\cdot t^{54}-\frac{254994760223921940386133350379054273681263861958395337695551592030}{630599616772381836353792302683359773510407161136439234579}\cdot t^{52}+\frac{219561547228761046016463213664041560208481380172376753919266398649735}{1891798850317145509061376908050079320531221483409317703737}\cdot t^{50}-\frac{46355559924206138373946286878836901135740395642657047032740031067790075}{1891798850317145509061376908050079320531221483409317703737}\cdot t^{48}+\frac{2490971936506414958503498543655968112160709885622155997769991604653134700}{630599616772381836353792302683359773510407161136439234579}\cdot t^{46}-\frac{314181154966361411181754390496538644685873726739416562963938834170148253500}{630599616772381836353792302683359773510407161136439234579}\cdot t^{44}+\frac{66636522948988214590611002978426139819228939897579989538855223480685620875}{1333191578799961599056643346053614743150966514030526923}\cdot t^{42}-\frac{5377390885873434245767995059054142182597521202866440505208295005055634545375}{1333191578799961599056643346053614743150966514030526923}\cdot t^{40}+\frac{351686400697283749820587081237755407374591645760581955159473088237393881214250}{1333191578799961599056643346053614743150966514030526923}\cdot t^{38}-\frac{18727810960010844244076698600733312527892288408540608837980327534442394329265250}{1333191578799961599056643346053614743150966514030526923}\cdot t^{36}+\frac{813939975701605990445592001924320648114817392855071683149695266666669265228038125}{1333191578799961599056643346053614743150966514030526923}\cdot t^{34}-\frac{28883406325853818945081525578502062224197983488492915396048542728371261264711735625}{1333191578799961599056643346053614743150966514030526923}\cdot t^{32}+\frac{835729602776548259235279911420593401161953458972660560679162025691199179091703905000}{1333191578799961599056643346053614743150966514030526923}\cdot t^{30}-\frac{19657361569620523733105034663237770750537910355628519589255079841446804069060609245000}{1333191578799961599056643346053614743150966514030526923}\cdot t^{28}+\frac{374086928643544282641895543344996431144184946216076574138335687366870284114445550725625}{1333191578799961599056643346053614743150966514030526923}\cdot t^{26}-\frac{5722317121751329112713433691832682566977476670677909304354242336946411964747346024203125}{1333191578799961599056643346053614743150966514030526923}\cdot t^{24}+\frac{69760540708199265454330820035097844988563932702122677970253082181453712429707818369656250}{1333191578799961599056643346053614743150966514030526923}\cdot t^{22}-\frac{670397587024113811311841716249996896290882335423591189665394903463226896643260416017531250}{1333191578799961599056643346053614743150966514030526923}\cdot t^{20}+\frac{5008260872676358522594146072793203305685298871235664655208135424330093515730241728502484375}{1333191578799961599056643346053614743150966514030526923}\cdot t^{18}-\frac{28570441701518965220123992454394398768480593178541301439016301573606454134906394077749796875}{1333191578799961599056643346053614743150966514030526923}\cdot t^{16}+\frac{121598807661440480246423315381926500882807813903184802725683440348013448572368373903634687500}{1333191578799961599056643346053614743150966514030526923}\cdot t^{14}-\frac{374361315273915153367799765686256171464797844540835499828656102144470928602542610505745937500}{1333191578799961599056643346053614743150966514030526923}\cdot t^{12}+\frac{799086745330153294035019062385132015234617843617258012336957057788978005113125654103971640625}{1333191578799961599056643346053614743150966514030526923}\cdot t^{10}-\frac{1113366501459433878685099928897545333556077967023342638749207092071416909409460631496502078125}{1333191578799961599056643346053614743150966514030526923}\cdot t^8+\frac{924854667020710851963642771555528461387271603697402409379816941693363187900865405076299593750}{1333191578799961599056643346053614743150966514030526923}\cdot t^6-\frac{394816847101503924860523558465382330085078985632750929579868584416291676854273839241731718750}{1333191578799961599056643346053614743150966514030526923}\cdot t^4+\frac{64945822705011873162067838694306759161249913484825142399511844723149137271651972818880234375}{1333191578799961599056643346053614743150966514030526923}\cdot t^2-\frac{1738573502600879937515969716334431816807563020346735078396880856652599805394380357183046875}{1333191578799961599056643346053614743150966514030526923}$

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 (probabilists') type can be downloaded here packed into a single file.