Rule: Q[2, 85]

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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^{87}-\frac{2032535416808816347262751591261858207033712002702480107222933}{548517893792217828944921385020718623807283708613048531883}\cdot t^{85}+\frac{3593321726399588246649955821872756355691810537898128997158739955}{548517893792217828944921385020718623807283708613048531883}\cdot t^{83}-\frac{48633759028537670616957300729022309428322083729955190373302108235}{6608649322797805168011101024346007515750406127868054601}\cdot t^{81}+\frac{39008618114987584509055816232884728416373432987995120406202164038850}{6608649322797805168011101024346007515750406127868054601}\cdot t^{79}-\frac{23800041891068919915283426070936066173855643738942491859100252095009070}{6608649322797805168011101024346007515750406127868054601}\cdot t^{77}+\frac{1044625149619257068019841845943139612924361027800252646559510394778025470}{600786302072527742546463729486000683250036920715277691}\cdot t^{75}-\frac{409952775248303264990339821801073615813087590472571732491353453861364360250}{600786302072527742546463729486000683250036920715277691}\cdot t^{73}+\frac{133300797826914601885290751674920825318243410021927798326023836044100199950875}{600786302072527742546463729486000683250036920715277691}\cdot t^{71}-\frac{36427921203014725481646484071349953898565617026159468842629509477714931753963125}{600786302072527742546463729486000683250036920715277691}\cdot t^{69}+\frac{8457332582017564582467565026033285295334225128896968359194687851296559460341602875}{600786302072527742546463729486000683250036920715277691}\cdot t^{67}-\frac{1682103644811382787955113842674502152619056257194841990909607048603360382171894781625}{600786302072527742546463729486000683250036920715277691}\cdot t^{65}+\frac{288475796377120749771269499953494419885161765670108179214320852109992800887955413465000}{600786302072527742546463729486000683250036920715277691}\cdot t^{63}-\frac{42873902677498795940616425292013595028218379424757279788339774634494024899655694116815000}{600786302072527742546463729486000683250036920715277691}\cdot t^{61}+\frac{5543575153305092980107197995907787525919017550234293631313274147673805133407000867627925000}{600786302072527742546463729486000683250036920715277691}\cdot t^{59}-\frac{625418264542588521702063494587465509481061325849448942025200091978349429272398400220646095000}{600786302072527742546463729486000683250036920715277691}\cdot t^{57}+\frac{61695314145668066387954952293061176503436264967766735852900288106326005261168613922018221113750}{600786302072527742546463729486000683250036920715277691}\cdot t^{55}-\frac{5328979838751246922832451202148156625156643769579155618358735150067665153196294048335887439006250}{600786302072527742546463729486000683250036920715277691}\cdot t^{53}+\frac{403347683691073485414647536592109663031249483009256517821823570883503769318515029495390365622943750}{600786302072527742546463729486000683250036920715277691}\cdot t^{51}-\frac{26757039630778566372695458450186051902237970757785896796334275384916487487753248612908422064710781250}{600786302072527742546463729486000683250036920715277691}\cdot t^{49}+\frac{1555102816036413131663926660146592259626723585262781403190904832153743266148778259969113818454614562500}{600786302072527742546463729486000683250036920715277691}\cdot t^{47}-\frac{79113329982260634858240121564735546926733557316911428229176188937143963358433162243840410737337058937500}{600786302072527742546463729486000683250036920715277691}\cdot t^{45}+\frac{3517915103827680147251529398786628724856402596374028475948639596718249979315778961174325456897253142812500}{600786302072527742546463729486000683250036920715277691}\cdot t^{43}-\frac{136460196247114323846594554540244457727080216846904327890029072791839761372798489395755508036728164608437500}{600786302072527742546463729486000683250036920715277691}\cdot t^{41}+\frac{4605802870762514952282027425058829420033141146656011091867693749859058730611951685537602781397185338592968750}{600786302072527742546463729486000683250036920715277691}\cdot t^{39}-\frac{134838753439349210611832280374581845679350471572908324671684443475348875208443465707587489892430534572826531250}{600786302072527742546463729486000683250036920715277691}\cdot t^{37}+\frac{3410983289218158475897108784680758137476146690240347387175129070786419856202747045445758792587288390103787468750}{600786302072527742546463729486000683250036920715277691}\cdot t^{35}-\frac{74221182539884489394737561330465966931845822259031291084829200903355173179577067564310658722189821730252442656250}{600786302072527742546463729486000683250036920715277691}\cdot t^{33}+\frac{1381745828619589807982700599019760149062542116459778619385861940844181264115669760048129522761711212351788060625000}{600786302072527742546463729486000683250036920715277691}\cdot t^{31}-\frac{21869306206972510792701425542633682365125382304895655987266723563781672411973249905497216555717875539937169184375000}{600786302072527742546463729486000683250036920715277691}\cdot t^{29}+\frac{292090376524938303790205888033330383669488708447403794981953943296503265637642292845013888335472498200628036768125000}{600786302072527742546463729486000683250036920715277691}\cdot t^{27}-\frac{3263350515359544144943039412476755205327822009850390935697331545853857812460308318584092629952601333775204540374375000}{600786302072527742546463729486000683250036920715277691}\cdot t^{25}+\frac{30182664251624513817370819619110844172076943935187148984244573108628993387215727105931613382452752769851484051693359375}{600786302072527742546463729486000683250036920715277691}\cdot t^{23}-\frac{228247533566775309781904943054599496922242600048206102588504416140731868333389821892719747419765654939296595786556640625}{600786302072527742546463729486000683250036920715277691}\cdot t^{21}+\frac{1390290430968534201836266367534215576185235655429272153604061531594550157253129545717423422663313032795402379621396484375}{600786302072527742546463729486000683250036920715277691}\cdot t^{19}-\frac{6697418656234633886288990602182513265045536498823945763155322609888863728308707439861036494861528803760334550875923828125}{600786302072527742546463729486000683250036920715277691}\cdot t^{17}+\frac{24941929638690066031402364991588737177356878623921278143668743069348511298746122311327514534622020889768656495129839843750}{600786302072527742546463729486000683250036920715277691}\cdot t^{15}-\frac{69761148391491236712608929082015438165140946842071259210418686738034362896600857681997303855195080036751851138643691406250}{600786302072527742546463729486000683250036920715277691}\cdot t^{13}+\frac{141100245216796427815073520185121871697468498750014253318555941759580394809707972127109597306992639320715780993697011718750}{600786302072527742546463729486000683250036920715277691}\cdot t^{11}-\frac{196034884215055103083613366134927931151797343335070092347414082624074651469744699079318274766830188261084023730682910156250}{600786302072527742546463729486000683250036920715277691}\cdot t^9+\frac{173774018811934488708295360346369438918755969589646537013332038028482333079372647566056867229111373578273520684767646484375}{600786302072527742546463729486000683250036920715277691}\cdot t^7-\frac{87645109230163587255319817429204354532165388627617800224239498429298709184279911833543244647063100784219507810983759765625}{600786302072527742546463729486000683250036920715277691}\cdot t^5+\frac{20543812786427351289558783170272931790613742776318712782274483580745442267387498092121671598419485593276746260862646484375}{600786302072527742546463729486000683250036920715277691}\cdot t^3-\frac{1410679703917378132507873109652629111445017453379724038984487768255199432919851696682372039529245485038291707313330078125}{600786302072527742546463729486000683250036920715277691}\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.