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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{52}-\frac{1550571682777332044635866459430470914756056617456}{40482020411384618043219305204899493414313061}\cdot t^{50}+\frac{17524624169708263623429071961348961895567756460774984}{1659762836866769339771991513400879229986835501}\cdot t^{48}-\frac{2956834255540507173942611946498393778802578555197637350}{1659762836866769339771991513400879229986835501}\cdot t^{46}+\frac{48897949746638785790060949731265618724079495721648866655}{237108976695252762824570216200125604283833643}\cdot t^{44}-\frac{57767876057473864822825345394666529287792625114667481049165}{3319525673733538679543983026801758459973671002}\cdot t^{42}+\frac{25685160867328618607139313640891121007554269120530543119645}{23132583092219781738982460117085424808178892}\cdot t^{40}-\frac{2537181742068409913914295178287396507034011059555062219113835}{46265166184439563477964920234170849616357784}\cdot t^{38}+\frac{197038963526263401126993860772220011116370195120970535504086725}{92530332368879126955929840468341699232715568}\cdot t^{36}-\frac{12153106968571775154867756749241050077094801066491402061269154175}{185060664737758253911859680936683398465431136}\cdot t^{34}+\frac{599045256741150959441916597224990383402317321272313000316599324825}{370121329475516507823719361873366796930862272}\cdot t^{32}-\frac{11836128753410428936201456347714056424975943814724228811016213340225}{370121329475516507823719361873366796930862272}\cdot t^{30}+\frac{375187009722816583454422993868165433035814693341031771801408804588675}{740242658951033015647438723746733593861724544}\cdot t^{28}-\frac{9523146971005637426495883232907412218835858733169852062450390480920375}{1480485317902066031294877447493467187723449088}\cdot t^{26}+\frac{192777169351650029296300419769224594852829503854298708658114858044875625}{2960970635804132062589754894986934375446898176}\cdot t^{24}-\frac{3092304002186597449945552375041688525321973191579320892411467566149486875}{5921941271608264125179509789973868750893796352}\cdot t^{22}+\frac{38949064139277880115669069119506272091526733952725959686233118861696436875}{11843882543216528250359019579947737501787592704}\cdot t^{20}-\frac{47559215098152095334597553997995482047780205783479170119359241464732611875}{2960970635804132062589754894986934375446898176}\cdot t^{18}+\frac{177201471916871540499971399268605056420094253809975847598598107391494303125}{2960970635804132062589754894986934375446898176}\cdot t^{16}-\frac{31529565569182270414682110838246329416757242071233328929038189968746991690625}{189502120691464452005744313279163800028601483264}\cdot t^{14}+\frac{126957445333610129324635097262221306877274629221127529257258151749259467871875}{379004241382928904011488626558327600057202966528}\cdot t^{12}-\frac{355156020357775734655648097863687596177942506598132333460438285783285172559375}{758008482765857808022977253116655200114405933056}\cdot t^{10}+\frac{650310631216898479262356899961877099524288716565542164778964632430095535490625}{1516016965531715616045954506233310400228811866112}\cdot t^8-\frac{712039729392315413194121441119861825350790883317773509577103617860684129859375}{3032033931063431232091909012466620800457623732224}\cdot t^6+\frac{401253925882513843243752621840528266021556760064046056253546344502323810015625}{6064067862126862464183818024933241600915247464448}\cdot t^4-\frac{86720426327224405950458476341784101866456955338684444866782958230861014859375}{12128135724253724928367636049866483201830494928896}\cdot t^2+\frac{2982596674546431351816170394147241760734082906434382750366146651493793515625}{24256271448507449856735272099732966403660989857792}$

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.