Rule: Q[26, 41]

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.

• $P_1$:
  $t^{26}-325\cdot t^{24}+44850\cdot t^{22}-3453450\cdot t^{20}+164038875\cdot t^{18}-5019589575\cdot t^{16}+100391791500\cdot t^{14}-1305093289500\cdot t^{12}+10767019638375\cdot t^{10}-53835098191875\cdot t^8+150738274937250\cdot t^6-205552193096250\cdot t^4+102776096548125\cdot t^2-7905853580625$
• $P_2$:
  $t^{67}-\frac{550640152744133860060576276506040808990097967633341732665}{347370223533358277498175832229340565547938809983077593}\cdot t^{65}+\frac{408858505985911643539987903870285705290751067551033581802880}{347370223533358277498175832229340565547938809983077593}\cdot t^{63}-\frac{21027884176011781087081609428500043842656930496715612148431440}{38596691503706475277575092469926729505326534442564177}\cdot t^{61}+\frac{20437741220947824061203594381571318740989138015704219351680265300}{115790074511119425832725277409780188515979603327692531}\cdot t^{59}-\frac{4932968861037107827297576813451477896559958780440130998760484386100}{115790074511119425832725277409780188515979603327692531}\cdot t^{57}+\frac{307301335069634428906882472994751130004049798713141151979318865482600}{38596691503706475277575092469926729505326534442564177}\cdot t^{55}-\frac{15208854811435065078834371645666060783676647605865792474481588099501000}{12865563834568825092525030823308909835108844814188059}\cdot t^{53}+\frac{1826574405257639351310103862093132799780491894335228578252881267804673000}{12865563834568825092525030823308909835108844814188059}\cdot t^{51}-\frac{179749907223957047089963190452558809598245981999795873875322252577135257000}{12865563834568825092525030823308909835108844814188059}\cdot t^{49}+\frac{14629993850785326144737514636003866780623411351809658578512746235485689049200}{12865563834568825092525030823308909835108844814188059}\cdot t^{47}-\frac{991446100154526902951541344680906951809825122399688973390628957979095013612000}{12865563834568825092525030823308909835108844814188059}\cdot t^{45}+\frac{56202373342415893433554400381916774358196825508353346561248018437559171444158500}{12865563834568825092525030823308909835108844814188059}\cdot t^{43}-\frac{2672899304851391749857656274923682704234077851730029300341428671885932355975154500}{12865563834568825092525030823308909835108844814188059}\cdot t^{41}+\frac{106810216195500526369720958109643202512580905224513738617184797590592021026058205000}{12865563834568825092525030823308909835108844814188059}\cdot t^{39}-\frac{3587159610050525818131538057405873972696021838119863377720631705705601418817884079000}{12865563834568825092525030823308909835108844814188059}\cdot t^{37}+\frac{101154564482678031684915789508759762709591161318969520999139063237581913934608252813750}{12865563834568825092525030823308909835108844814188059}\cdot t^{35}-\frac{2390035775068797575353896836482154589483337188145559429182323843339735245270874679653750}{12865563834568825092525030823308909835108844814188059}\cdot t^{33}+\frac{47161335939508999728159661582141197360708069210524417371381284260208240513942624799620000}{12865563834568825092525030823308909835108844814188059}\cdot t^{31}-\frac{773700909003251651097582238951720403388245279902471697026944618300062537374582836496950000}{12865563834568825092525030823308909835108844814188059}\cdot t^{29}+\frac{10491114369531941474186365072132741429858674474458994075250587060384335451335186711623177500}{12865563834568825092525030823308909835108844814188059}\cdot t^{27}-\frac{116714334753220583245949750351650112408446139841852156295154612072446449985036808939633437500}{12865563834568825092525030823308909835108844814188059}\cdot t^{25}+\frac{1055596079186636749677284517049004050370004577188654925900493620784864201563362961995517125000}{12865563834568825092525030823308909835108844814188059}\cdot t^{23}-\frac{7674049011859333052432970413038914193417069970035073126044377348158650202046298446686224875000}{12865563834568825092525030823308909835108844814188059}\cdot t^{21}+\frac{44220739824930198567564101048950270018777679326696054055527808906859045579494591830627908750000}{12865563834568825092525030823308909835108844814188059}\cdot t^{19}-\frac{198489065343557236239824367619931951936775001051752779995668352474912646209789169013559335750000}{12865563834568825092525030823308909835108844814188059}\cdot t^{17}+\frac{678926403410531940237153644047194727796097567339265523943253327053686766197725834589941443750000}{12865563834568825092525030823308909835108844814188059}\cdot t^{15}-\frac{1720483588199148355355856858544547169780073940148143618078035526972643551245547107447315995000000}{12865563834568825092525030823308909835108844814188059}\cdot t^{13}+\frac{3112658294144529498210048567373648237814994438640686166419134273559044921324534784140164444687500}{12865563834568825092525030823308909835108844814188059}\cdot t^{11}-\frac{3823058324670123598217903817626733199946279857415093664284863392272760952027254945444464292187500}{12865563834568825092525030823308909835108844814188059}\cdot t^9+\frac{2967725427944932187754581602608479502612093089912301055105503969256782997725782640932732911875000}{12865563834568825092525030823308909835108844814188059}\cdot t^7-\frac{1304682295573968489570578110411471899549046351602887910879118401849087727704797356645434665625000}{12865563834568825092525030823308909835108844814188059}\cdot t^5+\frac{266855148052301404998026147698827551689093317914562088399632586549891165138766978628262196484375}{12865563834568825092525030823308909835108844814188059}\cdot t^3-\frac{15665842203543451257435272427605365494450235123019359800244599736175521790675037906326058984375}{12865563834568825092525030823308909835108844814188059}\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.