Rule: Q[6, 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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{47}-\frac{527071428867678891335024735464482908526880}{16188442151594219121643968296810508779}\cdot t^{45}+\frac{3303060409196417247527898901971904568259280}{437525463556600516801188332346229967}\cdot t^{43}-\frac{120023300106815050037211253700575220449277914440}{113319095061159533851507778077673561453}\cdot t^{41}+\frac{11406994093435743440793267440002167516112171512300}{113319095061159533851507778077673561453}\cdot t^{39}-\frac{779185289814859325256469588150216864199911933238370}{113319095061159533851507778077673561453}\cdot t^{37}+\frac{1070577821541427234295366137199953464168653247574725}{3062678244896203617608318326423609769}\cdot t^{35}-\frac{11824505386910208941266386109693601651191263387707925}{875050927113201033602376664692459934}\cdot t^{33}+\frac{352183218545770880649230041970366452752185956083614475}{875050927113201033602376664692459934}\cdot t^{31}-\frac{16281101861549444934328550268016058383618939643725193625}{1750101854226402067204753329384919868}\cdot t^{29}+\frac{1529226247328797244003642299886625514238722297060505775}{9138913076900271891408633573811592}\cdot t^{27}-\frac{16376461923645147790354961782145200412372750954588465895375}{7000407416905608268819013317539679472}\cdot t^{25}+\frac{354203546400365121604641945172753717768282117849463386625625}{14000814833811216537638026635079358944}\cdot t^{23}-\frac{5876065341774861939076594689656341280695394214366516433486875}{28001629667622433075276053270158717888}\cdot t^{21}+\frac{73836091780555719678242928611866621150889659073352705470221875}{56003259335244866150552106540317435776}\cdot t^{19}-\frac{690641229656138952648624478229994942119763139372246584188233125}{112006518670489732301104213080634871552}\cdot t^{17}+\frac{9394927236451280538775336638150443127911117408636503629154696875}{448026074681958929204416852322539486208}\cdot t^{15}-\frac{45028446568573706963240603727893085176750713286060222262812315625}{896052149363917858408833704645078972416}\cdot t^{13}+\frac{145757518145355264926601197884629965623903839654680295194604590625}{1792104298727835716817667409290157944832}\cdot t^{11}-\frac{300643198216446261764642514833742816220412196165499414919380359375}{3584208597455671433635334818580315889664}\cdot t^9+\frac{364370741402025414221528140380709816134443203958022651197775103125}{7168417194911342867270669637160631779328}\cdot t^7-\frac{231735035799038062654492104636697525475208702693831741888999609375}{14336834389822685734541339274321263558656}\cdot t^5+\frac{66306062691762510099444243724060850693187666582382796261315484375}{28673668779645371469082678548642527117312}\cdot t^3-\frac{6486660812951389248492850895671098532993880187519949428960140625}{57347337559290742938165357097285054234624}\cdot t$

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.