Rule: Q[4, 7, 40]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{11}-328\cdot t^9+2112\cdot t^7-5040\cdot t^5+4095\cdot t^3-\frac{1575}{2}\cdot t$
• $P_3$:
  $16\cdot t^{51}-\frac{29985319106587111525672911604303195028401136952134327671055037849458613304}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{49}+\frac{7470648615900572956506989240682655475087837933642463713715895321424869231176}{3452008873983076440048795220156472902343624860042187456485826643003883}\cdot t^{47}-\frac{19290925641496568697801348158916395874647565180154709597569099878363282460952100}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{45}+\frac{2001898753310817709785174891898277834109774058030504081096443704561401313265247080}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{43}-\frac{150747932057308705591328633155604430240945622918742499712672334061117470463719095260}{58684150857712299480829518742660039339841622620717186760259052931066011}\cdot t^{41}+\frac{17081371493724236580226029093768517717487585707105482874126975023344469732280336590435}{117368301715424598961659037485320078679683245241434373520518105862132022}\cdot t^{39}-\frac{1490239604761277556284023881300987999248054267630379256607057526788681580114490153999755}{234736603430849197923318074970640157359366490482868747041036211724264044}\cdot t^{37}+\frac{203243452789597030050691503467992173492402919793280337313954326655047117550344679666447475}{938946413723396791693272299882560629437465961931474988164144846897056176}\cdot t^{35}-\frac{643377652424242744387387388894962754374675047510034930117480234163207897415365701165043775}{110464283967458446081561447045007132874995995521349998607546452576124256}\cdot t^{33}+\frac{6869213124055812834343561685388623364622591147412782760583068735507675238122893498577373525}{55232141983729223040780723522503566437497997760674999303773226288062128}\cdot t^{31}-\frac{233382779564287001195766580134886017387360923098171646733217685353903391156081217153335829525}{110464283967458446081561447045007132874995995521349998607546452576124256}\cdot t^{29}+\frac{3153115611443108353380841433058632509533825513515595982122142185013972766602378005167424883725}{110464283967458446081561447045007132874995995521349998607546452576124256}\cdot t^{27}-\frac{67571583060162864207677089986084633165124899988120884574136745745617188530419454489881104815125}{220928567934916892163122894090014265749991991042699997215092905152248512}\cdot t^{25}+\frac{2284673970486593790404958173748174722158550244035608975716902010950813322084743442477730785586875}{883714271739667568652491576360057062999967964170799988860371620608994048}\cdot t^{23}-\frac{30223577579853803707698946911854914734096666835295823598023084276869741367041161525268822107681875}{1767428543479335137304983152720114125999935928341599977720743241217988096}\cdot t^{21}+\frac{1237392422315911944795478818802237878077863954693368415553287163649238015212293309914139623933430625}{14139428347834681098439865221760913007999487426732799821765945929743904768}\cdot t^{19}-\frac{9650442168240241803482983592206329602512174607906942710175573206008188295616586249862587671322923125}{28278856695669362196879730443521826015998974853465599643531891859487809536}\cdot t^{17}+\frac{28093466994279845302929099515982517144915325340773029557003561495924249842408692010397063994461628125}{28278856695669362196879730443521826015998974853465599643531891859487809536}\cdot t^{15}-\frac{118799658055065871346874914364990729170247444497131630419963398218108161899884761330718367574878278125}{56557713391338724393759460887043652031997949706931199287063783718975619072}\cdot t^{13}+\frac{43941906223434071350971640601733118128045668885067289503161440457789728738793312654351426931253959375}{14139428347834681098439865221760913007999487426732799821765945929743904768}\cdot t^{11}-\frac{43208568228616220449626584242930985436339620232064541051883466499350957651399535897248811971550409375}{14139428347834681098439865221760913007999487426732799821765945929743904768}\cdot t^9+\frac{839500351766887719327194775399084803230309974577580575530959020713121901483634917912519157719498634375}{452461707130709795150075687096349216255983597655449594296510269751804952576}\cdot t^7-\frac{563200925155540506119997726991778912875292526285031084084045356089538958385241299806543029846026859375}{904923414261419590300151374192698432511967195310899188593020539503609905152}\cdot t^5+\frac{345717572934617183295563704991174356691094770989938268138052910489820546883088943143102889450063640625}{3619693657045678361200605496770793730047868781243596754372082158014439620608}\cdot t^3-\frac{31800727012789693990202343057044898831806179800030850595352023832416349573784452196817352698884453125}{7239387314091356722401210993541587460095737562487193508744164316028879241216}\cdot t$

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.