Rule: Q[2, 81]

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^{83}-\frac{1146103249708659305014703455017237711281779063967699812441}{342864931300254940565947220714331861629247314127176641}\cdot t^{81}+\frac{1823208163888132696599251399068638637851551819096200375205580}{342864931300254940565947220714331861629247314127176641}\cdot t^{79}-\frac{23266477822227085147970881613121578384546080209341451705337620}{4340062421522214437543635705244707109230978659837679}\cdot t^{77}+\frac{16701059019424027693170818620553650049941583322571226376891475050}{4340062421522214437543635705244707109230978659837679}\cdot t^{75}-\frac{9092392679098363143333520224315420358931178479465095361387306993850}{4340062421522214437543635705244707109230978659837679}\cdot t^{73}+\frac{3905075549858379221627269418029921443783412858127584116616732256708100}{4340062421522214437543635705244707109230978659837679}\cdot t^{71}-\frac{1358827502726444762198432227122439513476014187498557045055767537789014500}{4340062421522214437543635705244707109230978659837679}\cdot t^{69}+\frac{390419321575490607135900652530078340150414854638604221944968520243981138875}{4340062421522214437543635705244707109230978659837679}\cdot t^{67}-\frac{93933715422881533025663615711480484307276520153543369048314858597697664211875}{4340062421522214437543635705244707109230978659837679}\cdot t^{65}+\frac{19126518842506581701507721992558918394594367198314217255007016416868450757146000}{4340062421522214437543635705244707109230978659837679}\cdot t^{63}-\frac{3322732089535098204933816861286789726549681923069302822706795545936093882782506000}{4340062421522214437543635705244707109230978659837679}\cdot t^{61}+\frac{495569748839037543903514269024397769983286907573235623598129258148965646964329235000}{4340062421522214437543635705244707109230978659837679}\cdot t^{59}-\frac{63757500248847472182304409963698487885270435979534368590843917428732331331707869835000}{4340062421522214437543635705244707109230978659837679}\cdot t^{57}+\frac{7101105303656482958445707607855187343509348290273074398303989764598021904938603968250000}{4340062421522214437543635705244707109230978659837679}\cdot t^{55}-\frac{686451702315491054722762535505025959741688821009043846947925521289735245768188566755690000}{4340062421522214437543635705244707109230978659837679}\cdot t^{53}+\frac{57694618990379289291178326535814448579491379890330717913940990313032437063849591213880008750}{4340062421522214437543635705244707109230978659837679}\cdot t^{51}-\frac{4220143883912768362076904727594390228217235755344315088211892132873981956443545658694466218750}{4340062421522214437543635705244707109230978659837679}\cdot t^{49}+\frac{268728501111743215117941751046842858447544377235703320414709719495008034029093635788064876375000}{4340062421522214437543635705244707109230978659837679}\cdot t^{47}-\frac{14891681625664294452132700547825153612228382243007712852277620756137093117706467398944562519375000}{4340062421522214437543635705244707109230978659837679}\cdot t^{45}+\frac{717459231980827068163584505411477684763300586600191634284383942472407355659267330169119189292437500}{4340062421522214437543635705244707109230978659837679}\cdot t^{43}-\frac{30004549610124677120703814349341241426015738843374563742384103273189229885658774535890748956659937500}{4340062421522214437543635705244707109230978659837679}\cdot t^{41}+\frac{1086811310952750366113921176005042398814174228164160341483752343475147893269755644413531167021406875000}{4340062421522214437543635705244707109230978659837679}\cdot t^{39}-\frac{33998086063635408349202044165062603272058603357812314926064886513455498120638593768697298989170431875000}{4340062421522214437543635705244707109230978659837679}\cdot t^{37}+\frac{915249025040736137693364204991509890894202003307166606142469527549232435159239002981641919782896611718750}{4340062421522214437543635705244707109230978659837679}\cdot t^{35}-\frac{21111817651211034709973646088780274475532910769753987059461995213531780179804017287390024264268266985968750}{4340062421522214437543635705244707109230978659837679}\cdot t^{33}+\frac{415103618900267155885472243236409998201148219942347380590889918249803284487999278785206177011826844449250000}{4340062421522214437543635705244707109230978659837679}\cdot t^{31}-\frac{6914290648551462375096850788802080865058295877515613618017961764179374286573134240208385474049612803971250000}{4340062421522214437543635705244707109230978659837679}\cdot t^{29}+\frac{96853830643731249671964354355945737202570511079016601824962547687153756323201073069404191765874234326311875000}{4340062421522214437543635705244707109230978659837679}\cdot t^{27}-\frac{1131072650210229983160812229940197136327251789960480654214527313020379707150799537213143612050627866595146875000}{4340062421522214437543635705244707109230978659837679}\cdot t^{25}+\frac{10898799709049541513264696881929131085820122216887258863407148247238294670794067762414295927280882763442431250000}{4340062421522214437543635705244707109230978659837679}\cdot t^{23}-\frac{85586414443457617687583280016369083048936606875643126765202029392290853042912111568786464539227037929553181250000}{4340062421522214437543635705244707109230978659837679}\cdot t^{21}+\frac{539598676927435525899779194028458393858398717880699039385190157572435797136519024605371195246272915948675451171875}{4340062421522214437543635705244707109230978659837679}\cdot t^{19}-\frac{2681780092451980439664837039829199706533145848089039398573026713063989423381714279210284487851863503875046779296875}{4340062421522214437543635705244707109230978659837679}\cdot t^{17}+\frac{10269831799665361707759636660589187306836538814094189644963908620283246137314956269134582037710342136791464882812500}{4340062421522214437543635705244707109230978659837679}\cdot t^{15}-\frac{29437629688568404970579775485584727362621482707496665086907131164931603743309166264284078372039690774248227945312500}{4340062421522214437543635705244707109230978659837679}\cdot t^{13}+\frac{60809155285971570438741388810370767743588922774206649350998829016195849661792504729189556367054769465931132691406250}{4340062421522214437543635705244707109230978659837679}\cdot t^{11}-\frac{85973591267634355565787284426358678587812292320343572227570398052987225677103600190549509757872833080752543222656250}{4340062421522214437543635705244707109230978659837679}\cdot t^9+\frac{77262816266539270098541519109022332592906031044428243740590226857105396069313535948668970404128580216629539414062500}{4340062421522214437543635705244707109230978659837679}\cdot t^7-\frac{39349136142419097347865774272383590962140305366213047507381093883860910603734198130917845740915892184002579101562500}{4340062421522214437543635705244707109230978659837679}\cdot t^5+\frac{9273804343021570006821528794592635324332802350202721711688016403473959677151815380061176854517560293608851552734375}{4340062421522214437543635705244707109230978659837679}\cdot t^3-\frac{637340828080856025122679074713856554253453294550159625355909219706050612441713260540943337107766893259784755859375}{4340062421522214437543635705244707109230978659837679}\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.