Rule: Q[8, 11, 28]

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.

• $P_1$:
  $t^8-28\cdot t^6+210\cdot t^4-420\cdot t^2+105$
• $P_2$:
  $t^{19}-\frac{150851}{1347}\cdot t^{17}+\frac{6541430}{1347}\cdot t^{15}-\frac{47540390}{449}\cdot t^{13}+\frac{566981260}{449}\cdot t^{11}-\frac{3753992440}{449}\cdot t^9+\frac{13180991670}{449}\cdot t^7-\frac{21510616050}{449}\cdot t^5+\frac{12604959675}{449}\cdot t^3-\frac{2144332575}{449}\cdot t$
• $P_3$:
  $t^{47}-\frac{1194483575745888349515185867823172885300934124725225632047823528736960941417274358081537175438878857290515883617}{1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619}\cdot t^{45}+\frac{430482409435641653794510186565753436594887241888485716659293959095910642954899710943318581917121606225202527648615}{1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619}\cdot t^{43}-\frac{2521405736913832907768901096366818844714867478313709481676047876760859418357482596325318637041242327845714207381339295}{40574960503270819633672323725798625532824391996238759696370861221373048180312856121369521986078131660879950713}\cdot t^{41}+\frac{7004419198393201410048380090859791715906241018621818183481103325742292773209525845493925427740173648008588409410991048965}{770924249562145573039774150790173885123663447928536434231046363206087915425944266306020917735484501556719063547}\cdot t^{39}-\frac{244152415054285168553487567405279814931089644146027474721427907103043665082454193226281982113709097697297665126325854180125}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{37}+\frac{18912657640106506215672688566424074798940129691173964704671869992478131883195584464492301930888632273396403458894494837552675}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{35}-\frac{1109163450086076379467472552364002596378226034350448862252510851124950249379915134353042931929635908060072486861897054790330425}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{33}+\frac{1512596881374461495206085914053469862049143567392985690107030191333164968240867954518824238134523727372690058170534666642397050}{7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753}\cdot t^{31}-\frac{52634987244126811093775362210527403706558066405950339029177308603486487047546827272020969226251571068792192630352929752173280750}{7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753}\cdot t^{29}+\frac{34649675850026633149291439350952620166527582300502752410802993649255278963730472586400830476433511571205772631582157781363282450}{189929600779045472539978849664984943366263475715332947580942686180361644598655892167041369237616285182734433}\cdot t^{27}-\frac{9905998948762451216694177311939314877186129517408501868556223983425268957779068513002145309557094304733438263617334848146090982450}{2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251}\cdot t^{25}+\frac{159903873397677826500585661310242697546230406713968821835011212701442496370583685946448871932649314851698942656064751104835334256250}{2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251}\cdot t^{23}-\frac{1975694795440032130209921432661708161553608677480103940985832537969469475587152207185574407775019496396233060715948170539291080598750}{2595704543980288124713044278754794226005600834776216950272883377798275809514963859616232046247422564164037251}\cdot t^{21}+\frac{971369498499402062309323352840703743379390113793183857896518523737082500457448340130365316611686831801378025400979822291789335533750}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^{19}-\frac{6742192728423615679898044424262241649999924949833958031965305288906519012459698208746960080895923529294083154054141340680499293721250}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^{17}+\frac{33942952627386772681881020463923135608030554519899484620931610739981048372912732502311045589962470830964876248976846587455934074623125}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^{15}-\frac{119868461960642203569398623164698443108682277686155351706036330971069561504620258773007573513383977701108679016065113259880527979859375}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^{13}+\frac{283278436595349206763707735515524837563051285135611119182693365852765705866162873813281051302516051373499512261074026966614551586315625}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^{11}-\frac{418667837777642410288654889155512012648845994846673089485263494108112422629560319755006306019864812756886952793610568015479001963271875}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^9+\frac{350159195596690367225265420925996693975950985949315077468073968833597965055899277868416508231234375428044889217282310628638676311671875}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^7-\frac{141868284307233351915800133795887572636183750736354986968569779470325580908903492595364025518023810261607927101875169165721120782390625}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^5+\frac{20654718585953766957297460447266768104540193117786730514966459393805898521156417308775379322019290060370472385866977616215356621109375}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t^3-\frac{149581533247864174744375346975316623874146815318221828045695623595289777465459838088324379548023157448550525277180632365005767078125}{136616028630541480248054962039726011895031622882958786856467546199909253132366518927170107697232766534949329}\cdot t$

Warning: This rule has negative weights!

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.