Rule: Q[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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{52}-\frac{96910730173583252789741653714404432172253538591}{80964040822769236086438610409798986828626122}\cdot t^{50}+\frac{2190578021213532952928633995168620236945969557596873}{3319525673733538679543983026801758459973671002}\cdot t^{48}-\frac{1478417127770253586971305973249196889401289277598818675}{6639051347467077359087966053603516919947342004}\cdot t^{46}+\frac{48897949746638785790060949731265618724079495721648866655}{948435906781011051298280864800502417135334572}\cdot t^{44}-\frac{57767876057473864822825345394666529287792625114667481049165}{6639051347467077359087966053603516919947342004}\cdot t^{42}+\frac{25685160867328618607139313640891121007554269120530543119645}{23132583092219781738982460117085424808178892}\cdot t^{40}-\frac{2537181742068409913914295178287396507034011059555062219113835}{23132583092219781738982460117085424808178892}\cdot t^{38}+\frac{197038963526263401126993860772220011116370195120970535504086725}{23132583092219781738982460117085424808178892}\cdot t^{36}-\frac{12153106968571775154867756749241050077094801066491402061269154175}{23132583092219781738982460117085424808178892}\cdot t^{34}+\frac{599045256741150959441916597224990383402317321272313000316599324825}{23132583092219781738982460117085424808178892}\cdot t^{32}-\frac{11836128753410428936201456347714056424975943814724228811016213340225}{11566291546109890869491230058542712404089446}\cdot t^{30}+\frac{375187009722816583454422993868165433035814693341031771801408804588675}{11566291546109890869491230058542712404089446}\cdot t^{28}-\frac{9523146971005637426495883232907412218835858733169852062450390480920375}{11566291546109890869491230058542712404089446}\cdot t^{26}+\frac{192777169351650029296300419769224594852829503854298708658114858044875625}{11566291546109890869491230058542712404089446}\cdot t^{24}-\frac{3092304002186597449945552375041688525321973191579320892411467566149486875}{11566291546109890869491230058542712404089446}\cdot t^{22}+\frac{38949064139277880115669069119506272091526733952725959686233118861696436875}{11566291546109890869491230058542712404089446}\cdot t^{20}-\frac{190236860392608381338390215991981928191120823133916680477436965858930447500}{5783145773054945434745615029271356202044723}\cdot t^{18}+\frac{1417611775334972323999771194148840451360754030479806780788784859131954425000}{5783145773054945434745615029271356202044723}\cdot t^{16}-\frac{31529565569182270414682110838246329416757242071233328929038189968746991690625}{23132583092219781738982460117085424808178892}\cdot t^{14}+\frac{126957445333610129324635097262221306877274629221127529257258151749259467871875}{23132583092219781738982460117085424808178892}\cdot t^{12}-\frac{355156020357775734655648097863687596177942506598132333460438285783285172559375}{23132583092219781738982460117085424808178892}\cdot t^{10}+\frac{650310631216898479262356899961877099524288716565542164778964632430095535490625}{23132583092219781738982460117085424808178892}\cdot t^8-\frac{712039729392315413194121441119861825350790883317773509577103617860684129859375}{23132583092219781738982460117085424808178892}\cdot t^6+\frac{401253925882513843243752621840528266021556760064046056253546344502323810015625}{23132583092219781738982460117085424808178892}\cdot t^4-\frac{86720426327224405950458476341784101866456955338684444866782958230861014859375}{23132583092219781738982460117085424808178892}\cdot t^2+\frac{2982596674546431351816170394147241760734082906434382750366146651493793515625}{23132583092219781738982460117085424808178892}$

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.