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.

• $P_1$:
  $256\cdot t^8-3584\cdot t^6+13440\cdot t^4-13440\cdot t^2+1680$
• $P_2$:
  $256\cdot t^{19}-\frac{19308928}{1347}\cdot t^{17}+\frac{418651520}{1347}\cdot t^{15}-\frac{1521292480}{449}\cdot t^{13}+\frac{9071700160}{449}\cdot t^{11}-\frac{30031939520}{449}\cdot t^9+\frac{52723966680}{449}\cdot t^7-\frac{43021232100}{449}\cdot t^5+\frac{12604959675}{449}\cdot t^3-\frac{2144332575}{898}\cdot t$
• $P_3$:
  $256\cdot t^{47}-\frac{152893897695473708737943791081366129318519567964828880902121411678331000501411117834436758456176493733186033102976}{1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619}\cdot t^{45}+\frac{27550874203881065842848651940208219942072783480863085866194813382138281149113581500372389242695782798412961769511360}{1502776314935956282728604582436986130845347851712546655421143008199001784456031708198871184669560431884442619}\cdot t^{43}-\frac{80684983581242653048604835083738203030875759306038703413633532056347501387439443082410196385319754491062854636202857440}{40574960503270819633672323725798625532824391996238759696370861221373048180312856121369521986078131660879950713}\cdot t^{41}+\frac{112070707174291222560774081453756667454499856297949090935697653211876684371352413527902806843842778368137414550575856783440}{770924249562145573039774150790173885123663447928536434231046363206087915425944266306020917735484501556719063547}\cdot t^{39}-\frac{1953219320434281348427900539242238519448717153168219797771423256824349320659633545810255856909672781578381321010606833441000}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{37}+\frac{75650630560426024862690754265696299195760518764695858818687479969912527532782337857969207723554529093585613835577979350210700}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{35}-\frac{2218326900172152758934945104728005192756452068700897724505021702249900498759830268706085863859271816120144973723794109580660850}{256974749854048524346591383596724628374554482642845478077015454402029305141981422102006972578494833852239687849}\cdot t^{33}+\frac{1512596881374461495206085914053469862049143567392985690107030191333164968240867954518824238134523727372690058170534666642397050}{7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753}\cdot t^{31}-\frac{26317493622063405546887681105263701853279033202975169514588654301743243523773413636010484613125785534396096315176464876086640375}{7787113631940864374139132836264382678016802504328650850818650133394827428544891578848696138742267692492111753}\cdot t^{29}+\frac{17324837925013316574645719675476310083263791150251376205401496824627639481865236293200415238216755785602886315791078890681641225}{379859201558090945079957699329969886732526951430665895161885372360723289197311784334082738475232570365468866}\cdot t^{27}-\frac{4952999474381225608347088655969657438593064758704250934278111991712634478889534256501072654778547152366719131808667424073045491225}{10382818175921152498852177115019176904022403339104867801091533511193103238059855438464928184989690256656149004}\cdot t^{25}+\frac{79951936698838913250292830655121348773115203356984410917505606350721248185291842973224435966324657425849471328032375552417667128125}{20765636351842304997704354230038353808044806678209735602183067022386206476119710876929856369979380513312298008}\cdot t^{23}-\frac{987847397720016065104960716330854080776804338740051970492916268984734737793576103592787203887509748198116530357974085269645540299375}{41531272703684609995408708460076707616089613356419471204366134044772412952239421753859712739958761026624596016}\cdot t^{21}+\frac{485684749249701031154661676420351871689695056896591928948259261868541250228724170065182658305843415900689012700489911145894667766875}{4371712916177327367937758785271232380641011932254681179406961478397096100235728605669443446311448529118378528}\cdot t^{19}-\frac{3371096364211807839949022212131120824999962474916979015982652644453259506229849104373480040447961764647041577027070670340249646860625}{8743425832354654735875517570542464761282023864509362358813922956794192200471457211338886892622897058236757056}\cdot t^{17}+\frac{33942952627386772681881020463923135608030554519899484620931610739981048372912732502311045589962470830964876248976846587455934074623125}{34973703329418618943502070282169859045128095458037449435255691827176768801885828845355547570491588232947028224}\cdot t^{15}-\frac{119868461960642203569398623164698443108682277686155351706036330971069561504620258773007573513383977701108679016065113259880527979859375}{69947406658837237887004140564339718090256190916074898870511383654353537603771657690711095140983176465894056448}\cdot t^{13}+\frac{283278436595349206763707735515524837563051285135611119182693365852765705866162873813281051302516051373499512261074026966614551586315625}{139894813317674475774008281128679436180512381832149797741022767308707075207543315381422190281966352931788112896}\cdot t^{11}-\frac{418667837777642410288654889155512012648845994846673089485263494108112422629560319755006306019864812756886952793610568015479001963271875}{279789626635348951548016562257358872361024763664299595482045534617414150415086630762844380563932705863576225792}\cdot t^9+\frac{350159195596690367225265420925996693975950985949315077468073968833597965055899277868416508231234375428044889217282310628638676311671875}{559579253270697903096033124514717744722049527328599190964091069234828300830173261525688761127865411727152451584}\cdot t^7-\frac{141868284307233351915800133795887572636183750736354986968569779470325580908903492595364025518023810261607927101875169165721120782390625}{1119158506541395806192066249029435489444099054657198381928182138469656601660346523051377522255730823454304903168}\cdot t^5+\frac{20654718585953766957297460447266768104540193117786730514966459393805898521156417308775379322019290060370472385866977616215356621109375}{2238317013082791612384132498058870978888198109314396763856364276939313203320693046102755044511461646908609806336}\cdot t^3-\frac{149581533247864174744375346975316623874146815318221828045695623595289777465459838088324379548023157448550525277180632365005767078125}{4476634026165583224768264996117741957776396218628793527712728553878626406641386092205510089022923293817219612672}\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 (physicists') type can be downloaded here packed into a single file.