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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{58}-\frac{2226177299100671417968274674909530562368058572971486391253888}{11998724209199654391509790114482532688358698626274742307}\cdot t^{56}+\frac{8233972862800846933664161697010241380223050356291394294371198080}{131985966301196198306607691259307859571945684889022165377}\cdot t^{54}-\frac{8159832327165502092356267212129736757800443582668650806257650944960}{630599616772381836353792302683359773510407161136439234579}\cdot t^{52}+\frac{3512984755660176736263411418624664963335702082758028062708262378395760}{1891798850317145509061376908050079320531221483409317703737}\cdot t^{50}-\frac{370844479393649106991570295030695209085923165141256376261920248542320600}{1891798850317145509061376908050079320531221483409317703737}\cdot t^{48}+\frac{9963887746025659834013994174623872448642839542488623991079966418612538800}{630599616772381836353792302683359773510407161136439234579}\cdot t^{46}-\frac{628362309932722822363508780993077289371747453478833125927877668340296507000}{630599616772381836353792302683359773510407161136439234579}\cdot t^{44}+\frac{66636522948988214590611002978426139819228939897579989538855223480685620875}{1333191578799961599056643346053614743150966514030526923}\cdot t^{42}-\frac{5377390885873434245767995059054142182597521202866440505208295005055634545375}{2666383157599923198113286692107229486301933028061053846}\cdot t^{40}+\frac{175843200348641874910293540618877703687295822880290977579736544118696940607125}{2666383157599923198113286692107229486301933028061053846}\cdot t^{38}-\frac{9363905480005422122038349300366656263946144204270304418990163767221197164632625}{5332766315199846396226573384214458972603866056122107692}\cdot t^{36}+\frac{813939975701605990445592001924320648114817392855071683149695266666669265228038125}{21331065260799385584906293536857835890415464224488430768}\cdot t^{34}-\frac{28883406325853818945081525578502062224197983488492915396048542728371261264711735625}{42662130521598771169812587073715671780830928448976861536}\cdot t^{32}+\frac{104466200347068532404409988927574175145244182371582570084895253211399897386462988125}{10665532630399692792453146768428917945207732112244215384}\cdot t^{30}-\frac{2457170196202565466638129332904721343817238794453564948656884980180850508632576155625}{21331065260799385584906293536857835890415464224488430768}\cdot t^{28}+\frac{374086928643544282641895543344996431144184946216076574138335687366870284114445550725625}{341297044172790169358500696589725374246647427591814892288}\cdot t^{26}-\frac{5722317121751329112713433691832682566977476670677909304354242336946411964747346024203125}{682594088345580338717001393179450748493294855183629784576}\cdot t^{24}+\frac{34880270354099632727165410017548922494281966351061338985126541090726856214853909184828125}{682594088345580338717001393179450748493294855183629784576}\cdot t^{22}-\frac{335198793512056905655920858124998448145441167711795594832697451731613448321630208008765625}{1365188176691160677434002786358901496986589710367259569152}\cdot t^{20}+\frac{5008260872676358522594146072793203305685298871235664655208135424330093515730241728502484375}{5460752706764642709736011145435605987946358841469038276608}\cdot t^{18}-\frac{28570441701518965220123992454394398768480593178541301439016301573606454134906394077749796875}{10921505413529285419472022290871211975892717682938076553216}\cdot t^{16}+\frac{30399701915360120061605828845481625220701953475796200681420860087003362143092093475908671875}{5460752706764642709736011145435605987946358841469038276608}\cdot t^{14}-\frac{93590328818478788341949941421564042866199461135208874957164025536117732150635652626436484375}{10921505413529285419472022290871211975892717682938076553216}\cdot t^{12}+\frac{799086745330153294035019062385132015234617843617258012336957057788978005113125654103971640625}{87372043308234283355776178326969695807141741463504612425728}\cdot t^{10}-\frac{1113366501459433878685099928897545333556077967023342638749207092071416909409460631496502078125}{174744086616468566711552356653939391614283482927009224851456}\cdot t^8+\frac{462427333510355425981821385777764230693635801848701204689908470846681593950432702538149796875}{174744086616468566711552356653939391614283482927009224851456}\cdot t^6-\frac{197408423550751962430261779232691165042539492816375464789934292208145838427136919620865859375}{349488173232937133423104713307878783228566965854018449702912}\cdot t^4+\frac{64945822705011873162067838694306759161249913484825142399511844723149137271651972818880234375}{1397952692931748533692418853231515132914267863416073798811648}\cdot t^2-\frac{1738573502600879937515969716334431816807563020346735078396880856652599805394380357183046875}{2795905385863497067384837706463030265828535726832147597623296}$

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