Rule: Q[4, 15, 30]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{19}-\frac{748536}{667}\cdot t^{17}+\frac{226304664}{7337}\cdot t^{15}-\frac{3155515020}{7337}\cdot t^{13}+\frac{24226003620}{7337}\cdot t^{11}-\frac{9496214910}{667}\cdot t^9+\frac{1965071745}{58}\cdot t^7-\frac{112008278655}{2668}\cdot t^5+\frac{250467132825}{10672}\cdot t^3-\frac{83438061525}{21344}\cdot t$
• $P_3$:
  $16\cdot t^{49}-\frac{8592445836680086373465447652611370960567447151287783355867959395577337443182657718599891278944768657414700846356}{1137420755529850221718542737587247161471537838960260415721652995168689140649544237870882606666156878678875877}\cdot t^{47}+\frac{1853588024995569620980131042444321748496927664341266295337087617456537243764736315165412646736504447838994642698534}{1137420755529850221718542737587247161471537838960260415721652995168689140649544237870882606666156878678875877}\cdot t^{45}-\frac{2670434258537623899275254407600794195462315744702849309534489702376081179237291588853121671375532990089581295848361360}{12511628310828352438903970113459718776186916228562864572938182946855580547144986616579708673327725665467634647}\cdot t^{43}+\frac{645973171963149764776540274611000448354029431893863672605440174786777155288261147295880984663931689374586067623611652345}{33960133986534099477025061736533522392507344048956346697975067998608004342250677959287780684746683949126436899}\cdot t^{41}-\frac{166446750333940275765704890107801965599547798334590687991146978445545398665651923724869839057527014621207505102708949098705}{135840535946136397908100246946134089570029376195825386791900271994432017369002711837151122738986735796505747596}\cdot t^{39}+\frac{273210773745804578955625398740076707663938395138482095228886040338791425568826310281483633119815062133119231801019962317328535}{4618578222168637528875408396168559045380998790658063150924609247810688590546092202463138173125549017081195418264}\cdot t^{37}-\frac{10115086299084423035282479542008728064312451457649898256446710285777744227915268206538525381429956187687003070334721487391365315}{4618578222168637528875408396168559045380998790658063150924609247810688590546092202463138173125549017081195418264}\cdot t^{35}+\frac{25345196538138814330549762568421965773909479784950994510430105820954435838980590381367898591852938477271192652667021488201149575}{401615497579881524250035512710309482207043373100701143558661673722668573090964539344620710706569479746190905936}\cdot t^{33}-\frac{2398896644188816254838542148157557760913185923577980231233935283305228781633115027418068815588639103358844698994214457800944049575}{1679482989879504555954693962243112380138545014784750236699857908294795851107669891804777517500199642574980152096}\cdot t^{31}+\frac{2955654381124324765901818457587218363967089796775462186957040182774980547638418024892006541635572415628075386806963461518407393625}{115826413095138245238254756016766371044037587226534499082748821261710058697080682193432932241393078798274493248}\cdot t^{29}-\frac{41739575227623123124891450248330424060324314802131895839732841937670506475712362520455428407197531116207272368399949275032046380625}{115826413095138245238254756016766371044037587226534499082748821261710058697080682193432932241393078798274493248}\cdot t^{27}+\frac{919307951689787560893993762847050662203309971731892813286658332257791419037865169568676787053895841074866138089999195441817421125}{228905954733474792960977778689261602853829223767854741270254587473735293867748383781488008382199760470898208}\cdot t^{25}-\frac{1416448126282522970684006663864629938821597467281389284353157699248157348656704349759651061737459697543311478841496250126486045659375}{40287448033091563561132089049310042102273943383142434463564807395377411720723715545541889475267157842878084608}\cdot t^{23}+\frac{19331858313198078731062017767763864957599010506942246529094989748859605953552775966256501984763150584384037516329794883235864807703125}{80574896066183127122264178098620084204547886766284868927129614790754823441447431091083778950534315685756169216}\cdot t^{21}-\frac{2676103536715282786940233049820631086398174163293411017431513175018096142687040796347236461476347221438643435697058964848356470086875}{2120392001741661240059583634174212742224944388586443919134989862914600616880195555028520498698271465414636032}\cdot t^{19}+\frac{5029161016706303737884851787711643400947986979315548925689018599024411514532621142855443808740694611095926007543440073167973217520625}{997831530231369995322157004317276584576444418158326550181171700195106172649503790601656705269774807253946368}\cdot t^{17}-\frac{59753000415919973478858880827643471098056769887181347067590473370376609741615197584584859086569191162970700013955487439650330210695625}{3991326120925479981288628017269106338305777672633306200724686800780424690598015162406626821079099229015785472}\cdot t^{15}+\frac{256897599669911717503789602777219416777434396984505723286502101867323928036320383893208320188183028518345020645157290410114268050534375}{7982652241850959962577256034538212676611555345266612401449373601560849381196030324813253642158198458031570944}\cdot t^{13}-\frac{192571578444022914887642692605008941166190954495149651451502038984483307769406499283541201818326568447743921147898879381139276681759375}{3991326120925479981288628017269106338305777672633306200724686800780424690598015162406626821079099229015785472}\cdot t^{11}+\frac{69570340687228094119923886110440384623796006755928124357937047013892353545594183043961216880048408847061504672106428795109243674634375}{1451391316700174538650410188097856850293010062775747709354431563920154432944732786329682480392399719642103808}\cdot t^9-\frac{170372374403137084303215068694561738547948379726239041336866949587355289913305173043713943918330983463763185677279607654985444333315625}{5805565266800698154601640752391427401172040251102990837417726255680617731778931145318729921569598878568415232}\cdot t^7+\frac{115398443097450904539018295729776429018940596106809540331967086064043622318724341880459350814353749153556202760417558459133593492384375}{11611130533601396309203281504782854802344080502205981674835452511361235463557862290637459843139197757136830464}\cdot t^5-\frac{18129358188232164699096264494462024647148279258054150092654441852341768620837777004440793542583284927104122337518068016890092634390625}{11611130533601396309203281504782854802344080502205981674835452511361235463557862290637459843139197757136830464}\cdot t^3+\frac{1799858646221399258936722232789998753982341018292155311023827971840575675200939272649617863287288332958701518330910651862082747765625}{23222261067202792618406563009565709604688161004411963349670905022722470927115724581274919686278395514273660928}\cdot t$

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.