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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^9-117\cdot t^7+\frac{945}{2}\cdot t^5-\frac{2205}{4}\cdot t^3+\frac{945}{8}\cdot t$
• $P_3$:
  $8\cdot t^{55}-\frac{1645497558074402688597526632099383720044416897631390645936527900645930019}{310510137058770473110168530527155180031115053902860813535267697858977}\cdot t^{53}+\frac{82622128944557361464299610356798202348897581224870023985927464163183769143325}{50923662477638357590067639006453449525102868840069173419783902448872228}\cdot t^{51}-\frac{93237338040717301038263631407497033362152617628375153852987556451668180214194209}{305541974865830145540405834038720697150617213040415040518703414693233368}\cdot t^{49}+\frac{6901521019844332164712487727277212615069692472484371832667701412738174976441258427}{174595414209045797451660476593554684086066978880237166010687665538990496}\cdot t^{47}-\frac{1308673656836180611386972725815371540650193521690148573212698442833743514574115135115}{349190828418091594903320953187109368172133957760474332021375331077980992}\cdot t^{45}+\frac{62810069483922789383269456873843483907419797116200307715079179711158079633751314491715}{232793885612061063268880635458072912114755971840316221347583554051987328}\cdot t^{43}-\frac{171517644526137541713900740637808886075692320713390520986744399068374996120412718118135}{11355799298149320159457591973564532298280779114161766895004075807414016}\cdot t^{41}+\frac{15169187175710962124848005566077606806135657124052144816778325449507583980417585672054735}{22711598596298640318915183947129064596561558228323533790008151614828032}\cdot t^{39}-\frac{1070836391103558599850403709226083442917767824342395855220277126910009331429090990335701755}{45423197192597280637830367894258129193123116456647067580016303229656064}\cdot t^{37}+\frac{60732087029930600318020021008657726818371696839923951116179718742580408817152781699196536275}{90846394385194561275660735788516258386246232913294135160032606459312128}\cdot t^{35}-\frac{2776894271863390575013809713496902749421812662631125436316258589592213438367231382427576780275}{181692788770389122551321471577032516772492465826588270320065212918624256}\cdot t^{33}+\frac{51231287393260979561582584656544065610837920297178667982444390011147648305980184389161889827925}{181692788770389122551321471577032516772492465826588270320065212918624256}\cdot t^{31}-\frac{1523550110303124514759840072006685772444563490159509850967601442872787477873335813504588719805925}{363385577540778245102642943154065033544984931653176540640130425837248512}\cdot t^{29}+\frac{1254977255842028643368795233311609515434543016826374361151357254434018775480925353164240051924475}{25061074313157120351906409872694140244481719424357002802767615574982656}\cdot t^{27}-\frac{23949813638140019344028720226761191220163538513767680249960162445271016553639521073171075366378375}{50122148626314240703812819745388280488963438848714005605535231149965312}\cdot t^{25}+\frac{362360803422971347663673787471540991643607098527292327711245608621095047904789626741422281592541875}{100244297252628481407625639490776560977926877697428011211070462299930624}\cdot t^{23}-\frac{4303226876548030064231847604638875709171926975150706343610935016298060938622372431557120292737145625}{200488594505256962815251278981553121955853755394856022422140924599861248}\cdot t^{21}+\frac{19800599427693046752966666906820492596736369633746885309423197036018812142186765059228563898647174375}{200488594505256962815251278981553121955853755394856022422140924599861248}\cdot t^{19}-\frac{34738650274427711241897576077754055856298628025237127118091883726901944960256408742440693128462751875}{100244297252628481407625639490776560977926877697428011211070462299930624}\cdot t^{17}+\frac{2914981165134874586930532228277505535395913707232202146544067794298724668682326235620203032876017015625}{3207817512084111405044020463704849951293660086317696358754254793597779968}\cdot t^{15}-\frac{11134868109408269883317511954556486865298367817206824604208357394228581035173546587539664513811870365625}{6415635024168222810088040927409699902587320172635392717508509587195559936}\cdot t^{13}+\frac{29955230562361677500116632120136890197313181673145873111167621870269527960723076987434382327837906321875}{12831270048336445620176081854819399805174640345270785435017019174391119872}\cdot t^{11}-\frac{54190822487551331257879324045101666689030902681422279060289288252136137627836913499357343685039431009375}{25662540096672891240352163709638799610349280690541570870034038348782239744}\cdot t^9+\frac{61571962903981613433604771824251883145382626294357098214058450063258088844540956247118412208602982809375}{51325080193345782480704327419277599220698561381083141740068076697564479488}\cdot t^7-\frac{39312822969957584570531057194495880361551136014999373591512727096723175147049869187689084490808446671875}{102650160386691564961408654838555198441397122762166283480136153395128958976}\cdot t^5+\frac{11473603177450517814594605799316417956628835479498074113279585837530534843547725119852972777810103734375}{205300320773383129922817309677110396882794245524332566960272306790257917952}\cdot t^3-\frac{943903009182802754004932083792782045701244177630584131450687129825184586713402292425028357001724109375}{410600641546766259845634619354220793765588491048665133920544613580515835904}\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.