Rule: Q[3, 66]

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^{69}-\frac{29416145360067734608038557393760395427}{3224828964809030041731651376088176}\cdot t^{67}+\frac{31584683012233305857088598242248983406985}{6449657929618060083463302752176352}\cdot t^{65}-\frac{1328158750919508347882924755713486819008265}{806207241202257510432912844022044}\cdot t^{63}+\frac{628694089441573733036324006643837012328285635}{1612414482404515020865825688044088}\cdot t^{61}-\frac{445725537522582581140168920959332910421875266905}{6449657929618060083463302752176352}\cdot t^{59}+\frac{122977269948833281262141328792291710949845193870315}{12899315859236120166926605504352704}\cdot t^{57}-\frac{13548726049012350997482471513175556511659961150617175}{12899315859236120166926605504352704}\cdot t^{55}+\frac{2427611791991087034706879355360542386616348968378422925}{25798631718472240333853211008705408}\cdot t^{53}-\frac{1433267789663557929141053894190705665756229652970279162925}{206389053747777922670825688069643264}\cdot t^{51}+\frac{175919173566929922347490890423043058271589925063311401742375}{412778107495555845341651376139286528}\cdot t^{49}-\frac{4519493723801484124224748940455519671165691581421471800206625}{206389053747777922670825688069643264}\cdot t^{47}+\frac{390704723571565371980056889795486078016177248070410549387596875}{412778107495555845341651376139286528}\cdot t^{45}-\frac{57005477484426704401821379909675084830507178726044996763925304375}{1651112429982223381366605504557146112}\cdot t^{43}+\frac{3515483499542997663560106824057199249024195567115794485447133733125}{3302224859964446762733211009114292224}\cdot t^{41}-\frac{91679107836639592414208080267703051057138534908312769242976332464375}{3302224859964446762733211009114292224}\cdot t^{39}+\frac{4041614688384750080006873208892588004808953232359763906865292380093125}{6604449719928893525466422018228584448}\cdot t^{37}-\frac{32504532946603445954801517462103158699113037742122008652693826133053125}{2855978257266548551553047359233982464}\cdot t^{35}+\frac{1017258676499942237943286933726895294872632812335110011450254416814659375}{5711956514533097103106094718467964928}\cdot t^{33}-\frac{3334952065937852148269573578357637948839785292324824875481046614346884375}{1427989128633274275776523679616991232}\cdot t^{31}+\frac{72918247956154263624852339825002752516731329223197708679846804272283028125}{2855978257266548551553047359233982464}\cdot t^{29}-\frac{2640889267997800639027567632856696345286922482127271908184025290758705121875}{11423913029066194206212189436935929856}\cdot t^{27}+\frac{39284445676069562849129841916384703510651908283459344424650223933144806265625}{22847826058132388412424378873871859712}\cdot t^{25}-\frac{237617631426827887666908143830501937926770999973973927345459577866225092265625}{22847826058132388412424378873871859712}\cdot t^{23}+\frac{2308966089019172185766303400674967491598769888296787039005403204609206931171875}{45695652116264776824848757747743719424}\cdot t^{21}-\frac{70998356130705933071876723980594029021775048302762523955401312869521778094265625}{365565216930118214598790061981949755392}\cdot t^{19}+\frac{423655470601264361540114107017117873296814394205644753132223244191299567865296875}{731130433860236429197580123963899510784}\cdot t^{17}-\frac{478972121765115521827678729320642044524455438922106280998671599297461564310234375}{365565216930118214598790061981949755392}\cdot t^{15}+\frac{1591695635399062484212607186768425376698458930389141328810093897160935995185078125}{731130433860236429197580123963899510784}\cdot t^{13}-\frac{7462425759031548786384185711005969706314232914206204144983669321558517771595078125}{2924521735440945716790320495855598043136}\cdot t^{11}+\frac{11664815654697338521863658339811440955252442958136734047479654595552690635287734375}{5849043470881891433580640991711196086272}\cdot t^9-\frac{5602364952292357317303663605484350776797363236261860933058273478337605690571640625}{5849043470881891433580640991711196086272}\cdot t^7+\frac{2908244808880096034138011251907157288613652717174654702514680072254683013090234375}{11698086941763782867161281983422392172544}\cdot t^5-\frac{10375455116694945836584209758619196993716537263284669904047845693819695959965234375}{374338782136441051749161023469516549521408}\cdot t^3+\frac{586793765457355774739240758726528971676756750344501233328366321474199602308203125}{748677564272882103498322046939033099042816}\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.