Rule: Q[8, 57]

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^{65}-\frac{120745293344100042666672443051962701529777807413832609056920756625354565924}{65202874584476169921118250946389252606779483770759927787696562618863753}\cdot t^{63}+\frac{1779129675479509946936359511014070441524982943409576811195735779578188210831610}{1108448867936094888659010266088617294315251224102918772390841564520683801}\cdot t^{61}-\frac{4801091854835998947542253432599692039638055535127577878946041302358020085530200614}{5542244339680474443295051330443086471576256120514593861954207822603419005}\cdot t^{59}+\frac{1810990442237015615123244720841539497324964025231094129969203333576045989757315534242}{5542244339680474443295051330443086471576256120514593861954207822603419005}\cdot t^{57}-\frac{459716945157297345630861064827198004006077584594508992269709264693250327700225906848}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{55}+\frac{22016599067145295860792972883482241410250878463672273148327749702771714892974933922056746}{1108448867936094888659010266088617294315251224102918772390841564520683801}\cdot t^{53}-\frac{290801350806069864016747509287828032885306665607911316084156292270355904185610320047781018}{85265297533545760666077712776047484178096248007916828645449351116975677}\cdot t^{51}+\frac{2368516973530881356247490914672324882338134192995554958581497805020827861918731931572440230}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{49}-\frac{267757449600931068577403079825069863774134237744635280861545877968503146499794494894291031740}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{47}+\frac{24933116068237451670145921438173157681437588843285901434396050489520071908182968428209762213450}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{45}-\frac{1924205833974416350976833096875397238058467615332427968638342568717729118416502616490733471130150}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{43}+\frac{123573117962034586613747757587531174110803385343877300404239619774206420713208860077173721963513850}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{41}-\frac{6619118144435606193447707384011996382837784279311650466399867425550573903699971039575155890264147800}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{39}+\frac{295962461018094592688643383960284560155822299429871495616094843830302937701605388910877556533241050650}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{37}-\frac{11040811758850366023653547179143397720453377885016346632521531763242780428817620260916218662640366762250}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{35}+\frac{343004276033811015708330176627502902624982299560103439024390757302086809241970032152989728216382651522000}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{33}-\frac{8846623563628030133246366570283673570840043043825448426500722461193470474094669936864802942651079626835500}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{31}+\frac{188578840037495814680543718782914460941072571392350454828829994299148926896711720430945317657240171354935750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{29}-\frac{3302636232319413490633417584693411868475629834613674603820529650084118316630143324866339349367130576745917250}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{27}+\frac{47158785274168015057619640891550384434572880067995030538903666230099061469716867749088737289979659363011243750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{25}-\frac{543765729960742063556205546554666816966468460326068276910368407783720149794211658788187271649393986643404950000}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{23}+\frac{5002150549008473728243325935083905348025159249389053165309632348921952701936811047772070008287723684671175393750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{21}-\frac{36157379239298667822216867882103522746474729670917103098066503232924735243467589917346678529689712250832276318750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{19}+\frac{201451026706608500994061879187828564116878691079917552609291716720226625270315108371692096500725235737419882956250}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{17}-\frac{843983978271085618252602543142460155145063649394415606825053712981281981664879265669623186939960802076447871062500}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{15}+\frac{2574136971787751950965204869112093484039271741442834430725531263989198445689299475351564045298235098206877320968750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{13}-\frac{5472390365648819391235628090360324378798785233952738275946996821908743031181614459130267138401113705338363661031250}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^{11}+\frac{7633279920803494917077413765293649015720974301202223985083877534083639621689426657636321518388993282337696861918750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^9-\frac{6396587040654265753148578761653271413784111806818814287405079358082601631800488482014867027708356870188642264975000}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^7+\frac{2806658213910419072533271290751446984517085437565622327481224434329246108294202466119907319190085079267894963718750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^5-\frac{508673896265197623902975098066677999815402994313448072075114896597232665506295437188588643105274482391417685718750}{5015605737267397686239865457414557892829191059289225214438197124527981}\cdot t^3+\frac{23270915602450934142077562143182542938272392550678590423645658174729245035333428693639312259456298319569959671875}{5015605737267397686239865457414557892829191059289225214438197124527981}\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.