Rule: Q[4, 87]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{91}-\frac{188600573418355610940843693731017599108915671660485968744382303829572297812492936287905462239}{48146351331333056377914400096978706685040808452769592461818697991623541506793021229899439}\cdot t^{89}+\frac{29290352471705509842376544502221944134946861403433289403167822906707744842379415250435433632413836}{3996147160500643679366895208049232654858387101579876174330951933304753945063820762081653437}\cdot t^{87}-\frac{34867996166306104263905492900461850889771207078881276207595002879131826115167922204909647783592028980}{3996147160500643679366895208049232654858387101579876174330951933304753945063820762081653437}\cdot t^{85}+\frac{4239326701360448587547522731915180549407333338017927070679577186895694802817869310300448294966209821815}{570878165785806239909556458292747522122626728797125167761564561900679135009117251725950491}\cdot t^{83}-\frac{33110927073780573073564713287324930313232427778149894690147784951893914738281872307171734373705128646765}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{81}+\frac{17009910554263766626466667681518875845947647318896688299653819046817187185224411058812894384253728936007440}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{79}-\frac{7113486936294381629024789711469834737386284498516447093119261169047318693884520026774839298903253738367366720}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{77}+\frac{2468739152435106343659715426213870444118558661401900650465114641187605085792471804500392565128957520289511867175}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{75}-\frac{721264923515634752006689590007229225522213297791720923369964023598165376947208963899312430343565569198170570916375}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{73}+\frac{179339903472608204050339488103056314373710227967388351048022120750579636379605543261435973709359096539741488855274500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{71}-\frac{38272699993289852648072042213267697214433286610688381169358344461327887331606515119765515848641810226375286236870099500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{69}+\frac{7056624890650629592828579500213259209123515621348860126422059415423951499606155072927540014075064693459451569679083322875}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{67}-\frac{1129910072996391600267843202566089294800948981373215357070007900073856125358656378930439037771286375190109098787854926846875}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{65}+\frac{157751927492836363123078644089931461918950017271563060706497337976623183487206333066685184777755557850897637195145158975120000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{63}-\frac{19263031600819356629390097691369551043374879900959964562875691727426503670545509506725267899274542410939610829360856382496440000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{61}+\frac{2061972215481940349325924280845395964029909105980764830013221840711229889235187399224808711538283003726394064131148652176382396250}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{59}-\frac{193793040874302218387314166044561164944005603389566309920590175375182099873319757303124049136341309284906405852616546890874358576250}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{57}+\frac{16007111786980985949116695775366176564005009330606258890747902859374793940358797675347321978991884011778973834992324196710057935575000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{55}-\frac{1162482025814602374009075047060997577160353243855754795181172473068050615101980148364418273732550148565248149521815575171843459553425000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{53}+\frac{74218072436684871742469354608979750909168946809102055263500753312168027085099617211642555222066254964310778497450311610041747184037781250}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{51}-\frac{4163102269746959998222009421564010933210617402609863293589369454853184012238660138084443706457658344913943192318753959630755268866766781250}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{49}+\frac{204940796292876324606045355138593775843651870859844043047427491437045185114511010050041054032379908243719022272422639642783607603443300500000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{47}-\frac{8839926891962160566188665345030641084852069085366536668025500948943275879273853598065787217848606257318186963330558059216342287439241085000000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{45}+\frac{333397150167101646491673986026482058563085689945014179724689898814726057246218263967471211211674805595751376156132448612015522636086363110468750}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{43}-\frac{10965290327588911759857919347115531239727652295634480290503797789661011131612163511131578868607078136605191512270834451590809958327292785121968750}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{41}+\frac{313492461074525770811138031307816510033965850912574309436778641510916477574134355654634391377280783161999008757294311033581921819639961104432125000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{39}-\frac{7760959461034324522715463948934028088278887196486681635641988261802784572122279007237056045740044484457929351449135538213680068985405777002146375000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{37}+\frac{165621523386712084029116083859842740986861985427919383307863992582155568597477784861440204185858238523904210612912206503554999476859082648616693593750}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{35}-\frac{3030562275973107065348534274935984007740185589045811025925279666769215715137647405925202233745524236285883120648117469238424925393358791151099618593750}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{33}+\frac{47253862229149944690311152189566986694806013041142038118247656517203743183548598723596519782942673431058221665431174682158919603464374244152562680000000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{31}-\frac{623316025795692720800843890805494300040053278638060304512436011151742587053146419346153127089227595719023764186826562907850541859012702617425809905000000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{29}+\frac{6896832608765179754242512694451303763134471477993081983704298525515678133706657488756030268190526179450104104864844218799057376010785094315524306876328125}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{27}-\frac{63377115749277619941460932814151812999058748827919919052592265714787076186850500928662109898518935772387168891771872125237381006389615228236113735492578125}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{25}+\frac{478018922800810409809806040325280604110518030497918071445199372274894686473584056118158972013180866809049495912561883939214029113831473129971455012179687500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{23}-\frac{2918151286338931924774101489985177292242697488315733839398349829678757973725072001177807767554281981657010066151685236853180335974896146860170624717570312500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{21}+\frac{14178268900992376909061629623563795442445886148514793681514935582252807694329166237769693331834453190026376291801124573215753835803019826087680366280900390625}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{19}-\frac{53719990937704838632316857888459994888577232954283618874951626004598249936117896029493194662862872878421075811150981051898441061820386170475097562164712890625}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{17}+\frac{154796530594520339058960255504112627222646988003696897309470738518507539497312771027236631580060947683125408885413918895337551231358373887665388302232031250000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{15}-\frac{328792053532939283532288627558891081950101845098237309663728032510571838856395721167684602936543479098977664112505080181218807366902479354751451912198750000000}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{13}+\frac{494758512344032489103007513670803065136777951960106967769578041869908101132190871600876426879242880277495411669774982538971141679847108276650855804776748046875}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^{11}-\frac{501068524919753515335540185741995640016156370710421326726477029157985355234517882013577239243531938760808324706771503698824512803137331544377864080675966796875}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^9+\frac{319008120622412400901320384591094630945657722872824912198142073128700872286745228615182515473664976066021647863822843598485584412085222824561239548117695312500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^7-\frac{115963238012449865449348848950717027352395839970584134388691488251198977168638285660705667835364363151914204812557872115299049037616968638952602339705273437500}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^5+\frac{20512576918338343880668819390906217226075272135332810511283498425688422277540757524941453394845054186744812104233686166743270287249957105054593888703662109375}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\cdot t^3-\frac{1191984315825747626014569572955905433023281637822013060685093466426638036645329429825430099048278508522155579521971275876709006992345446694816004198974609375}{6878050190190436625416342870996958097862972636109941780259813998803363072399003032842777}\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.