Rule: Q[2, 65]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{67}-\frac{73876849581392695235921922450150564637391042}{17201262424585284698480207686516181275521}\cdot t^{65}+\frac{37278652695060015998285470585473819350702675440}{17201262424585284698480207686516181275521}\cdot t^{63}-\frac{186730275306945124115106297733824949631470380040}{273035911501353725372701709309780655167}\cdot t^{61}+\frac{41370393298953337874687490665018044211285974332650}{273035911501353725372701709309780655167}\cdot t^{59}-\frac{6848489000378893639836399530277783297357237278449765}{273035911501353725372701709309780655167}\cdot t^{57}+\frac{880260993071813865518731331233540237611738098361554295}{273035911501353725372701709309780655167}\cdot t^{55}-\frac{180252047057636256036391994933728702223188714779085059975}{546071823002707450745403418619561310334}\cdot t^{53}+\frac{119722715277376698859080634372740266346980618764136398325025}{4368574584021659605963227348956490482672}\cdot t^{51}-\frac{16327334102039285785454017766786706388809430181443451963030625}{8737149168043319211926454697912980965344}\cdot t^{49}+\frac{461402136069636053436625402524595126326820217516246876402471625}{4368574584021659605963227348956490482672}\cdot t^{47}-\frac{43513262013818344569832345454983602972116116900145347505843831625}{8737149168043319211926454697912980965344}\cdot t^{45}+\frac{6877740828190905101569793098208279007408928750022021576062387036875}{34948596672173276847705818791651923861376}\cdot t^{43}-\frac{456764727843377720327144309561451535580775729615585762671959176586875}{69897193344346553695411637583303847722752}\cdot t^{41}+\frac{12762450615325756609522933193271550727351986739458742758118171811834375}{69897193344346553695411637583303847722752}\cdot t^{39}-\frac{600122063812772442484724310505397826030016887884661353276513863395624375}{139794386688693107390823275166607695445504}\cdot t^{37}+\frac{189736429387074685316852235180639288360905595069740251162562683082447998125}{2236710187019089718253172402665723127128064}\cdot t^{35}-\frac{6287127403357365155020194623704338522883544826586089508941618737895357778125}{4473420374038179436506344805331446254256128}\cdot t^{33}+\frac{21756092519946093187818723725649773828163110694347990833042993082318463946875}{1118355093509544859126586201332861563564032}\cdot t^{31}-\frac{500716516885555740808525327970441709403960474548123624314974927286557182046875}{2236710187019089718253172402665723127128064}\cdot t^{29}+\frac{19040640608788058085608588988223967850870465964960495192427613232453165242571875}{8946840748076358873012689610662892508512256}\cdot t^{27}-\frac{296715186278091244577678972902745181298999427086037004972438228113919534371821875}{17893681496152717746025379221325785017024512}\cdot t^{25}+\frac{1876224990258189572796721469821001590552741033737798829967634200062843975153828125}{17893681496152717746025379221325785017024512}\cdot t^{23}-\frac{19023310814823327258201949368356146394735345710778798886355085292838602375497578125}{35787362992305435492050758442651570034049024}\cdot t^{21}+\frac{609285135788229922547398689903844635268668901765463372507316803474507235850606640625}{286298903938443483936406067541212560272392192}\cdot t^{19}-\frac{3780840048514280794834867399100133163575748812991094482506686452425697577742178640625}{572597807876886967872812135082425120544784384}\cdot t^{17}+\frac{4438529696925397817736459377491190259425741518800702419236657036496770481425041046875}{286298903938443483936406067541212560272392192}\cdot t^{15}-\frac{15294548678086452489003691718396614561964566139990922943708371487339923755044368046875}{572597807876886967872812135082425120544784384}\cdot t^{13}+\frac{74256827551008279778894040254586487593380765985883636575003808401500551887237545078125}{2290391231507547871491248540329700482179137536}\cdot t^{11}-\frac{120053942363452880989337400295915552765956627777585568711815150880843785707402661328125}{4580782463015095742982497080659400964358275072}\cdot t^9+\frac{59565582243616793990532351789534729161162943762959233937794537013925707942716331953125}{4580782463015095742982497080659400964358275072}\cdot t^7-\frac{31905638079109646681829275207481376126380326711184182568338698499556388183252013203125}{9161564926030191485964994161318801928716550144}\cdot t^5+\frac{117301989320781519431005754078002581846961038237302484926340972529041322671706749609375}{293170077632966127550879813162201661718929604608}\cdot t^3-\frac{6825071658728618677533193828963480278365494810789459728271677505481882220650312109375}{586340155265932255101759626324403323437859209216}\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.