Rule: Q[9, 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.

• $P_1$:
  $512\cdot t^9-9216\cdot t^7+48384\cdot t^5-80640\cdot t^3+30240\cdot t$
• $P_2$:
  $512\cdot t^{23}-\frac{847253248}{18099}\cdot t^{21}+\frac{10526171264}{6033}\cdot t^{19}-\frac{69724285120}{2011}\cdot t^{17}+\frac{2436061827136}{6033}\cdot t^{15}-\frac{5743770803680}{2011}\cdot t^{13}+\frac{24755471460720}{2011}\cdot t^{11}-\frac{63531751923640}{2011}\cdot t^9+\frac{92322361281150}{2011}\cdot t^7-\frac{70208873169435}{2011}\cdot t^5+\frac{50216778386775}{4022}\cdot t^3-\frac{12961617443775}{8044}\cdot t$
• $P_3$:
  $512\cdot t^{45}-\frac{34677099786119231968743058286002307948939055387566165113921187784277227793435702579793348504704}{204271955048849590532690866692237528408040228848772905028076191305061920752041272059722365}\cdot t^{43}+\frac{5198653433651058340847979074450230968388291170474387668567857749745757233151718614497375622721344}{204271955048849590532690866692237528408040228848772905028076191305061920752041272059722365}\cdot t^{41}-\frac{3274645125077229612961371859722112870557066706156270759020610258037961201152316151168569474479504672}{1429903685341947133728836066845662698856281601941410335196533339135433445264288904418056555}\cdot t^{39}+\frac{13201965246086207687411514192209136408238803987142642866564215925785887437805269567887246804656057168}{95326912356129808915255737789710846590418773462760689013102222609028896350952593627870437}\cdot t^{37}-\frac{2846236837791305207323448009056313748858899369107580705117576362185247936330916153778008006776135539056}{476634561780649044576278688948554232952093867313803445065511113045144481754762968139352185}\cdot t^{35}+\frac{18121197863304184423018767021976832479698664716097681954632803184047821826023210380403475526961199929624}{95326912356129808915255737789710846590418773462760689013102222609028896350952593627870437}\cdot t^{33}-\frac{1015236440406965936403180929538704759561394794331999850107460629609496514025205143350761284386431703257320}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{31}+\frac{18624887481442113594821862501980658838708552413897859961818867862600198348863420304012724092228373275453416}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{29}-\frac{262866898558767601693584693460520904689763279321107377080694833696315852324140179326421382659086034769056795}{222429462164302887468930054842658642044310471413108274363905186087734091485556051798364353}\cdot t^{27}+\frac{5720933260018283665202858965151661655251442251093937389787056268970170131827984560572466872289318117593751863}{444858924328605774937860109685317284088620942826216548727810372175468182971112103596728706}\cdot t^{25}-\frac{670699372642836733449522642334154770525476271485127365043872652568402252134501613258781161522701279109883064575}{6228024940600480849130041535594441977240693199567031682189345210456554561595569450354201884}\cdot t^{23}+\frac{8594689820094003564264105793238253509091978856889775735017959063359610316503801198262443228388900171809062486825}{12456049881200961698260083071188883954481386399134063364378690420913109123191138900708403768}\cdot t^{21}-\frac{156883730624901369472100754681364487001567411001268211970362269542216667899031334277088044720811531233487992125}{46827255192484818414511590493191293061960099244864899866085302334259808733801274062813548}\cdot t^{19}+\frac{1138644523372056712766376556335379513091717624843142899334513685125075695918302130852163577313369774722785372375}{93654510384969636829023180986382586123920198489729799732170604668519617467602548125627096}\cdot t^{17}-\frac{12125523442336740512765885902242091093847261028083431181382537505858398705902535092593919077766361675162850980375}{374618041539878547316092723945530344495680793958919198928682418674078469870410192502508384}\cdot t^{15}+\frac{13208631100780159633338435488841025037868189758092396435748211784359082276626962791756128458443008959385521509875}{214067452308502027037767270826017339711817596547953827959247096385187697068805824287147648}\cdot t^{13}-\frac{9987701322658323633921953447971413208855299030478383196336387453027313408944575702882086939375289157117449570375}{122324258462001158307295583329152765549610055170259330262426912220107255467889042449798656}\cdot t^{11}+\frac{864217671869053100570647824334525126768516029334095905571409507469003683027896631597510634500678328506759189033875}{11987777329276113514114967166256971023861785406685414365717837397570511035853126160080268288}\cdot t^9-\frac{967265096650991242580710722007314951065518460364621702343911064891245771252826962730696804165763245479052964615625}{23975554658552227028229934332513942047723570813370828731435674795141022071706252320160536576}\cdot t^7+\frac{91039500355906638688105225238515190409931008329002830334304727556557452059994192437727833496906995702499097559125}{6850158473872064865208552666432554870778163089534522494695907084326006306201786377188724736}\cdot t^5-\frac{15583902748701588185896410705426655070902553580007975919334471969213352754124923049795938062141523990060697073125}{6850158473872064865208552666432554870778163089534522494695907084326006306201786377188724736}\cdot t^3+\frac{2077470924148033391100194284450587236520913656325347919425636556480521319990287543652411234335264671447150173125}{13700316947744129730417105332865109741556326179069044989391814168652012612403572754377449472}\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.