Rule: Q[1, 8, 56]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_3$:
  $t^{65}-\frac{48756443636972876374566540204142356882643669712300959510316795886366760}{26329924825818023815358945523436194015742759935352760191605320169273}\cdot t^{63}+\frac{352147391716550764534728933632364551360256506850921085386870828070433729736}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{61}-\frac{190055865180448873620334332250996546060645845422126689488165600555172498558584}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{59}+\frac{71691014093182081569160060161596688044894179049908515755256295198907204654369826}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{57}-\frac{20110666305136701511349154363733708590242440296431382669003709537775618122079393424}{219416040215150198461324546028634950131189666127939668263377668077275}\cdot t^{55}+\frac{174342463024952625767982702365450104193890419393012943824473075491967155172297060916}{8776641608606007938452981841145398005247586645117586730535106723091}\cdot t^{53}-\frac{8806342050168413454388470861125417495331831453010643915331115067380958666252209835616}{2581365179001767040721465247395705295661054895622819626627972565615}\cdot t^{51}+\frac{243938068990255569493177456514257856093214027851320073670258077325702012491104739789778}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{49}-\frac{27588432847543021393249192045475228917891375845694210587674310097759324166922604149168552}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{47}+\frac{2570514811110673899959217118831983155861924427577669495460844119516194295806964512609478688}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{45}-\frac{198542173434241760006793273548950793372750486426622309669312528478123191746702675897524653000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{43}+\frac{12764792631695491168303768651446342837925350383773734808028364296854386328505546754967121257650}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{41}-\frac{684778321570689616894870887700332387583382699729967268116704152036656788003933889859088837976480}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{39}+\frac{30681142653034822341595648470379491608699244437826879876728398325720730297944663417996519774007420}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{37}-\frac{1147666358822824301775333194623809705397650139994708849480509175598697933756130590163808878253836880}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{35}+\frac{35783276140417776082132319358379865526402233238502025134830564231599196660344468559448250657864694000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{33}-\frac{5552821387379644868343761282927898402747558253689642640679034031950262131929916665633006786070492600}{3091455304193732982899958380114617120552161551644095361231104869}\cdot t^{31}+\frac{19892133803454280907289902947000608913289038864483243220617021923974596121291370804276432827927132188200}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{29}-\frac{351282116871222486747727644103169100145399832974563805526928385178765823109223343820293598307074674601800}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{27}+\frac{30366390342499539596682623585753242004599516204599974891864513892470273696596257360271303313991720179850}{3091455304193732982899958380114617120552161551644095361231104869}\cdot t^{25}-\frac{59322374286515339269937577871104637838643375212544803659181112725503020995972179405968973749039121627050000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{23}+\frac{556181305750644761132069417762859846564187590747276171005058042132961113481271579608269982890876554977867500}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{21}-\frac{4122488265185475745443700782764914619675626900037763566102982295577793241813232364387811937014407500493960000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{19}+\frac{23745920377940428940976239001006679626184976696108510111005820053469538699062890661807895617985952736098458750}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{17}-\frac{104001870657076416926111329651187232849788576668028194619159309058539660948468673590403869277771325363954335000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{15}+\frac{336756022432678449001520854087089676891192708770310396755370036676965917942897298723216998221686863696804750000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{13}-\frac{776851948782061738383992057158142894656426946411642511090435326405284254161283485204588531042016507546897555000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^{11}+\frac{1214166510787433280148358462747105038406062578511241949363560502237991447798588920796016599390068451584714213750}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^9-\frac{1197002942258902096434305784982866492536764907377359280400771848910301037408999917688255588584366299394052680000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^7+\frac{667175063209050911362539829588369660780528380784358187010396807872877211385293075599695270352445988942444382500}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^5-\frac{173570650606242281712680551044222801718754137021511008630737156131793139744177662303898577058706288206848250000}{516273035800353408144293049479141059132210979124563925325594513123}\cdot t^3+\frac{13556758378337454458626117896759264645633286272527541101598186980644171057071585514880117385709841584287628125}{516273035800353408144293049479141059132210979124563925325594513123}\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.