Rule: Q[3, 6, 46]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^9-\frac{117}{4}\cdot t^7+\frac{945}{4}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{4}\cdot t$
• $P_3$:
  $t^{55}-\frac{1645497558074402688597526632099383720044416897631390645936527900645930019}{1242040548235081892440674122108620720124460215611443254141070791435908}\cdot t^{53}+\frac{82622128944557361464299610356798202348897581224870023985927464163183769143325}{101847324955276715180135278012906899050205737680138346839567804897744456}\cdot t^{51}-\frac{93237338040717301038263631407497033362152617628375153852987556451668180214194209}{305541974865830145540405834038720697150617213040415040518703414693233368}\cdot t^{49}+\frac{6901521019844332164712487727277212615069692472484371832667701412738174976441258427}{87297707104522898725830238296777342043033489440118583005343832769495248}\cdot t^{47}-\frac{1308673656836180611386972725815371540650193521690148573212698442833743514574115135115}{87297707104522898725830238296777342043033489440118583005343832769495248}\cdot t^{45}+\frac{62810069483922789383269456873843483907419797116200307715079179711158079633751314491715}{29099235701507632908610079432259114014344496480039527668447944256498416}\cdot t^{43}-\frac{171517644526137541713900740637808886075692320713390520986744399068374996120412718118135}{709737456134332509966099498347783268642548694635110430937754737963376}\cdot t^{41}+\frac{15169187175710962124848005566077606806135657124052144816778325449507583980417585672054735}{709737456134332509966099498347783268642548694635110430937754737963376}\cdot t^{39}-\frac{1070836391103558599850403709226083442917767824342395855220277126910009331429090990335701755}{709737456134332509966099498347783268642548694635110430937754737963376}\cdot t^{37}+\frac{60732087029930600318020021008657726818371696839923951116179718742580408817152781699196536275}{709737456134332509966099498347783268642548694635110430937754737963376}\cdot t^{35}-\frac{2776894271863390575013809713496902749421812662631125436316258589592213438367231382427576780275}{709737456134332509966099498347783268642548694635110430937754737963376}\cdot t^{33}+\frac{51231287393260979561582584656544065610837920297178667982444390011147648305980184389161889827925}{354868728067166254983049749173891634321274347317555215468877368981688}\cdot t^{31}-\frac{1523550110303124514759840072006685772444563490159509850967601442872787477873335813504588719805925}{354868728067166254983049749173891634321274347317555215468877368981688}\cdot t^{29}+\frac{1254977255842028643368795233311609515434543016826374361151357254434018775480925353164240051924475}{12236852691971250171829301695651435666250839562674317774788874792472}\cdot t^{27}-\frac{23949813638140019344028720226761191220163538513767680249960162445271016553639521073171075366378375}{12236852691971250171829301695651435666250839562674317774788874792472}\cdot t^{25}+\frac{362360803422971347663673787471540991643607098527292327711245608621095047904789626741422281592541875}{12236852691971250171829301695651435666250839562674317774788874792472}\cdot t^{23}-\frac{4303226876548030064231847604638875709171926975150706343610935016298060938622372431557120292737145625}{12236852691971250171829301695651435666250839562674317774788874792472}\cdot t^{21}+\frac{19800599427693046752966666906820492596736369633746885309423197036018812142186765059228563898647174375}{6118426345985625085914650847825717833125419781337158887394437396236}\cdot t^{19}-\frac{34738650274427711241897576077754055856298628025237127118091883726901944960256408742440693128462751875}{1529606586496406271478662711956429458281354945334289721848609349059}\cdot t^{17}+\frac{2914981165134874586930532228277505535395913707232202146544067794298724668682326235620203032876017015625}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^{15}-\frac{11134868109408269883317511954556486865298367817206824604208357394228581035173546587539664513811870365625}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^{13}+\frac{29955230562361677500116632120136890197313181673145873111167621870269527960723076987434382327837906321875}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^{11}-\frac{54190822487551331257879324045101666689030902681422279060289288252136137627836913499357343685039431009375}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^9+\frac{61571962903981613433604771824251883145382626294357098214058450063258088844540956247118412208602982809375}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^7-\frac{39312822969957584570531057194495880361551136014999373591512727096723175147049869187689084490808446671875}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^5+\frac{11473603177450517814594605799316417956628835479498074113279585837530534843547725119852972777810103734375}{24473705383942500343658603391302871332501679125348635549577749584944}\cdot t^3-\frac{943903009182802754004932083792782045701244177630584131450687129825184586713402292425028357001724109375}{24473705383942500343658603391302871332501679125348635549577749584944}\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.