Rule: Q[5, 58]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{63}-\frac{10386226931623322076655036100418944253766785230463920}{353429722047178973897232293879307462896964020043}\cdot t^{61}+\frac{120426240177749823363225211280438699428440984823740707896}{9542602495273832295225271934741301498218028541161}\cdot t^{59}-\frac{32170159144405461233347102339047256082524853210547504322988}{9542602495273832295225271934741301498218028541161}\cdot t^{57}+\frac{181796092121388282887000595570269106716331425192994386757154}{289169772584055524097735513173978833279334198217}\cdot t^{55}-\frac{2797555997741546110578111450094738369517132702477494814692145}{32129974731561724899748390352664314808814910913}\cdot t^{53}+\frac{597761427540893388947509622635488748301273118114172654885595495}{64259949463123449799496780705328629617629821826}\cdot t^{51}-\frac{33677272684417316104023143596358381784060352099194273289829543825}{42839966308748966532997853803552419745086547884}\cdot t^{49}+\frac{4580975376691293591614884577546777472381008223458508620038600965575}{85679932617497933065995707607104839490173095768}\cdot t^{47}-\frac{507621939558803512971383935838903666934126111519736612130162431739975}{171359865234995866131991415214209678980346191536}\cdot t^{45}+\frac{5134853279038428223376145987051103491438245649691078226928622945378625}{38079970052221303584886981158713261995632487008}\cdot t^{43}-\frac{1158841809771094211249163551869824997287036691621652887446669817764626375}{228479820313327821509321886952279571973794922048}\cdot t^{41}+\frac{72293270503811687272428466036233225070828501432079263250708139411358197125}{456959640626655643018643773904559143947589844096}\cdot t^{39}-\frac{1248866563316560964516133258938355958561873579162972279011034887539790157375}{304639760417770428679095849269706095965059896064}\cdot t^{37}+\frac{17925647217422785437912953698992106951713323730508396599688720040319419889875}{203093173611846952452730566179804063976706597376}\cdot t^{35}-\frac{640517689686014401662490628162406306269101500664749779978347826115568753769375}{406186347223693904905461132359608127953413194752}\cdot t^{33}+\frac{18939957910858003290363781067919674953131636158789570366310882347770369012261875}{812372694447387809810922264719216255906826389504}\cdot t^{31}-\frac{461534236322837044929456749680151933554362900783188113175409838685369605176511875}{1624745388894775619621844529438432511813652779008}\cdot t^{29}+\frac{9215601236307726379449116873318046697612466139246672433961591913596014944791068125}{3249490777789551239243689058876865023627305558016}\cdot t^{27}-\frac{149665137729423753565474777534072071669813876195906769790215066062848945780142935625}{6498981555579102478487378117753730047254611116032}\cdot t^{25}+\frac{1958566813983962337141040530833658766218438303189821129281912242187782107988629296875}{12997963111158204956974756235507460094509222232064}\cdot t^{23}-\frac{20414218810375807008793403203980777939101522805603186417294368746242706265680757671875}{25995926222316409913949512471014920189018444464128}\cdot t^{21}+\frac{167055804965005260202232463495384326632065874906996681144745461318761647277345698953125}{51991852444632819827899024942029840378036888928256}\cdot t^{19}-\frac{1054353326338231825103578301775936946678204299331513015465827321637386123615526140515625}{103983704889265639655798049884059680756073777856512}\cdot t^{17}+\frac{5019268276982009321712994465357408878906208092410675132729696608137631113377008712484375}{207967409778531279311596099768119361512147555713024}\cdot t^{15}-\frac{17522114313187843748625008209462981382576247935430350973476935996542006806286157500984375}{415934819557062558623192199536238723024295111426048}\cdot t^{13}+\frac{43251515449320393689269373841458674813355352498019668048369962946184974397073054609765625}{831869639114125117246384399072477446048590222852096}\cdot t^{11}-\frac{910176455723588730945697508039939012147394581423262711247838873545056618835289772796875}{21059990863648737145478086052467783444268106907648}\cdot t^9+\frac{75184188224446359481676096412775253459648841604772417710360547863034650068913392056109375}{3327478556456500468985537596289909784194360891408384}\cdot t^7-\frac{44524760954396483135651423494396494619353223516009861004763500882639284215639394722234375}{6654957112913000937971075192579819568388721782816768}\cdot t^5+\frac{12396054309779174121416696030538436515359150195034654652337360674598167130974215249140625}{13309914225826001875942150385159639136777443565633536}\cdot t^3-\frac{1046255755876800847612104387793456308428958207687884014197105744609823744016489513203125}{26619828451652003751884300770319278273554887131267072}\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.