Rule: Q[5, 62]

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.

• $P_1$:
  $t^5-10\cdot t^3+15\cdot t$
• $P_2$:
  $t^{67}-\frac{37081342617759730339696957543708050816471959120964229307}{17611964765029972453417171637800543410212110687536561}\cdot t^{65}+\frac{1063650918764407732175971208481107241554918715397601005060570}{510746978185869201149097977496215758896151209938560269}\cdot t^{63}-\frac{219227484983494218068284002976965896359559011414670918218115070}{170248992728623067049699325832071919632050403312853423}\cdot t^{61}+\frac{1612359584875629490339079196011997912600803893209943497787044150}{2885576147942763848299988573424947790373735649370397}\cdot t^{59}-\frac{18018905494154818824479441051644212390063197739881899526768923830}{99502625791129787872413399083618889323232263771393}\cdot t^{57}+\frac{4532241546325933662669652966341077294551528795225319348310381371010}{99502625791129787872413399083618889323232263771393}\cdot t^{55}-\frac{907655827811439127767248582796658575002357629449642245290560407992050}{99502625791129787872413399083618889323232263771393}\cdot t^{53}+\frac{147329956513733944130215580547315154396810170626311363787952870702409650}{99502625791129787872413399083618889323232263771393}\cdot t^{51}-\frac{19631332332452592921150635857003512726472281185056521218922481300890791250}{99502625791129787872413399083618889323232263771393}\cdot t^{49}+\frac{2167069134565921948320526363918857035952489128052095330590608769656502850250}{99502625791129787872413399083618889323232263771393}\cdot t^{47}-\frac{199473041576891795989794315120295134155984113700328248107743143654790011114250}{99502625791129787872413399083618889323232263771393}\cdot t^{45}+\frac{15378375526519348019375795058629788627604836041426812432388234671074154966553750}{99502625791129787872413399083618889323232263771393}\cdot t^{43}-\frac{995735446414368821710442276170528738397576982075830583175789062497137439121498750}{99502625791129787872413399083618889323232263771393}\cdot t^{41}+\frac{54218697469390400021174153829380782049064455712089760730200908007991090126094006250}{99502625791129787872413399083618889323232263771393}\cdot t^{39}-\frac{2482719464316014837515353699320097334408402838825229314369556030953096073617822216250}{99502625791129787872413399083618889323232263771393}\cdot t^{37}+\frac{95489282558570055857493325632831127872554380578078563580004724214212739635655053332500}{99502625791129787872413399083618889323232263771393}\cdot t^{35}-\frac{3077438234784149583945152340149216880697384781685939349876340738702577894704074720575000}{99502625791129787872413399083618889323232263771393}\cdot t^{33}+\frac{82806590688154285427312603324455571239845463925076861712286411408832177362198643557943750}{99502625791129787872413399083618889323232263771393}\cdot t^{31}-\frac{1851210786108903782233303238727534082516047273519383691831259801446134835317794350438843750}{99502625791129787872413399083618889323232263771393}\cdot t^{29}+\frac{34168188942629904270870754845085871223884989315661730520238300768060147459747274359295206250}{99502625791129787872413399083618889323232263771393}\cdot t^{27}-\frac{516562549512199619955681463332159477438163456092719761641691134874540779548664062405363381250}{99502625791129787872413399083618889323232263771393}\cdot t^{25}+\frac{6334266153857830506187001886335015115587659495102082704559017046475895051001192283364892343750}{99502625791129787872413399083618889323232263771393}\cdot t^{23}-\frac{62242166645840694860368939111191882535673717023768175173141148765797698445935469412289478593750}{99502625791129787872413399083618889323232263771393}\cdot t^{21}+\frac{482825868761631682615019777613010616073087928784882904508258597455109661386833382158025586718750}{99502625791129787872413399083618889323232263771393}\cdot t^{19}-\frac{2902169928120288078829175511073132533886684035648677496718402031427279002516742408659386032468750}{99502625791129787872413399083618889323232263771393}\cdot t^{17}+\frac{13203071608965449490014408904889020554832651115875978385812318854865120964303984357894452916968750}{99502625791129787872413399083618889323232263771393}\cdot t^{15}-\frac{44108703779515693663724657861786916124552630503538623496882633266592643059435349107049932402968750}{99502625791129787872413399083618889323232263771393}\cdot t^{13}+\frac{103979207364248941659788677873041665071945536628933304594328235106667895799445614777569923787031250}{99502625791129787872413399083618889323232263771393}\cdot t^{11}-\frac{163763750069831751241167159674244714736273506685132211277773984746007549884618969173455920403906250}{99502625791129787872413399083618889323232263771393}\cdot t^9+\frac{159267334524239942915229002098630792078085716137178661450966715313523869434193176803068646625468750}{99502625791129787872413399083618889323232263771393}\cdot t^7-\frac{84606180121842355311963974968209223947244806555999015164920398863740668150460431685243127764218750}{99502625791129787872413399083618889323232263771393}\cdot t^5+\frac{19771967520806277939824949230047225176698178039626859507324581100557143354143629347836444948046875}{99502625791129787872413399083618889323232263771393}\cdot t^3-\frac{1246679625980249332935359478454768162693741581530239066635354896244432718400275531573457398828125}{99502625791129787872413399083618889323232263771393}\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.