Rule: Q[1, 8, 14, 22]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^9-36\cdot t^7+378\cdot t^5-1260\cdot t^3+945\cdot t$
• $P_3$:
  $t^{23}-\frac{3309583}{18099}\cdot t^{21}+\frac{82235713}{6033}\cdot t^{19}-\frac{1089441955}{2011}\cdot t^{17}+\frac{76126932098}{6033}\cdot t^{15}-\frac{358985675230}{2011}\cdot t^{13}+\frac{3094433932590}{2011}\cdot t^{11}-\frac{15882937980910}{2011}\cdot t^9+\frac{46161180640575}{2011}\cdot t^7-\frac{70208873169435}{2011}\cdot t^5+\frac{50216778386775}{2011}\cdot t^3-\frac{12961617443775}{2011}\cdot t$
• $P_4$:
  $t^{45}-\frac{270914842079056499755805142859393030851086370215360664952509279564665842136216426404635535193}{408543910097699181065381733384475056816080457697545810056152382610123841504082544119444730}\cdot t^{43}+\frac{81228959900797786575749673038284858881067049538662307321372777339777456767995603351521494105021}{408543910097699181065381733384475056816080457697545810056152382610123841504082544119444730}\cdot t^{41}-\frac{102332660158663425405042870616316027204908334567383461219394070563686287536009879724017796077484521}{2859807370683894267457672133691325397712563203882820670393066678270866890528577808836113110}\cdot t^{39}+\frac{825122827880387980463219637013071025514925249196415179160263495361617964862829347992952925291003573}{190653824712259617830511475579421693180837546925521378026204445218057792701905187255740874}\cdot t^{37}-\frac{177889802361956575457715500566019609303681210569223794069848522636577996020682259611125500423508471191}{476634561780649044576278688948554232952093867313803445065511113045144481754762968139352185}\cdot t^{35}+\frac{2265149732913023052877345877747104059962333089512210244329100398005977728252901297550434440870149991203}{95326912356129808915255737789710846590418773462760689013102222609028896350952593627870437}\cdot t^{33}-\frac{253809110101741484100795232384676189890348698582999962526865157402374128506301285837690321096607925814330}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{31}+\frac{9312443740721056797410931250990329419354276206948929980909433931300099174431710152006362046114186637726708}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{29}-\frac{262866898558767601693584693460520904689763279321107377080694833696315852324140179326421382659086034769056795}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{27}+\frac{5720933260018283665202858965151661655251442251093937389787056268970170131827984560572466872289318117593751863}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{25}-\frac{670699372642836733449522642334154770525476271485127365043872652568402252134501613258781161522701279109883064575}{1557006235150120212282510383898610494310173299891757920547336302614138640398892362588550471}\cdot t^{23}+\frac{8594689820094003564264105793238253509091978856889775735017959063359610316503801198262443228388900171809062486825}{1557006235150120212282510383898610494310173299891757920547336302614138640398892362588550471}\cdot t^{21}-\frac{627534922499605477888403018725457948006269644005072847881449078168866671596125337108352178883246124933951968500}{11706813798121204603627897623297823265490024811216224966521325583564952183450318515703387}\cdot t^{19}+\frac{4554578093488226851065506225341518052366870499372571597338054740500302783673208523408654309253479098891141489500}{11706813798121204603627897623297823265490024811216224966521325583564952183450318515703387}\cdot t^{17}-\frac{24251046884673481025531771804484182187694522056166862362765075011716797411805070185187838155532723350325701960750}{11706813798121204603627897623297823265490024811216224966521325583564952183450318515703387}\cdot t^{15}+\frac{13208631100780159633338435488841025037868189758092396435748211784359082276626962791756128458443008959385521509875}{1672401971160172086232556803328260466498574973030889280931617940509278883350045502243341}\cdot t^{13}-\frac{9987701322658323633921953447971413208855299030478383196336387453027313408944575702882086939375289157117449570375}{477829134617192024637873372379502990428164278008825508837605125859793966671441572069526}\cdot t^{11}+\frac{864217671869053100570647824334525126768516029334095905571409507469003683027896631597510634500678328506759189033875}{23413627596242409207255795246595646530980049622432449933042651167129904366900637031406774}\cdot t^9-\frac{967265096650991242580710722007314951065518460364621702343911064891245771252826962730696804165763245479052964615625}{23413627596242409207255795246595646530980049622432449933042651167129904366900637031406774}\cdot t^7+\frac{91039500355906638688105225238515190409931008329002830334304727556557452059994192437727833496906995702499097559125}{3344803942320344172465113606656520932997149946061778561863235881018557766700091004486682}\cdot t^5-\frac{15583902748701588185896410705426655070902553580007975919334471969213352754124923049795938062141523990060697073125}{1672401971160172086232556803328260466498574973030889280931617940509278883350045502243341}\cdot t^3+\frac{2077470924148033391100194284450587236520913656325347919425636556480521319990287543652411234335264671447150173125}{1672401971160172086232556803328260466498574973030889280931617940509278883350045502243341}\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.