Rule: Q[6, 39]

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^{45}-\frac{309106933635763395386939518658804826720}{10905070395460721410598644805409721}\cdot t^{43}+\frac{1056418412425757162882161652024051977589040}{185386196722832263980176961691965257}\cdot t^{41}-\frac{1407042195778894925601080948183462934116008440}{2039248163951154903781946578611617827}\cdot t^{39}+\frac{16402123313447287159951330182966463822880785560}{291321166278736414825992368373088261}\cdot t^{37}-\frac{6694671824239063081912513348989535458161439199860}{2039248163951154903781946578611617827}\cdot t^{35}+\frac{2425351217010781982476109949914452470707555392200}{17136539192866847930940727551358133}\cdot t^{33}-\frac{7174604599156983066788182528942202817405428161950}{1557867199351531630085520686487103}\cdot t^{31}+\frac{356709202468537478260665543950373455297997881495325}{3115734398703063260171041372974206}\cdot t^{29}-\frac{13630231900164422941189747395406813607444020070425575}{6231468797406126520342082745948412}\cdot t^{27}+\frac{400749824910407603385994492279480109393785974330601275}{12462937594812253040684165491896824}\cdot t^{25}-\frac{9038460957620293179993674433690519661297415349981298125}{24925875189624506081368330983793648}\cdot t^{23}+\frac{9703599324074170881472058643180140352904426801863268125}{3115734398703063260171041372974206}\cdot t^{21}-\frac{501970622881466594109034816821225790290348205413136145625}{24925875189624506081368330983793648}\cdot t^{19}+\frac{9614488805681918576726420596337367419609792763813449731875}{99703500758498024325473323935174592}\cdot t^{17}-\frac{66647914714145534356516691559905349358151432042883517336875}{199407001516996048650946647870349184}\cdot t^{15}+\frac{1296981356592082893691869923813386274864644667644460818359375}{1595256012135968389207573182962793472}\cdot t^{13}-\frac{4246021766847439435279913592239737053710175103456785363703125}{3190512024271936778415146365925586944}\cdot t^{11}+\frac{8826108208950043300659734483356338566893539535189633120378125}{6381024048543873556830292731851173888}\cdot t^9-\frac{10735517765412670192671527674991336573659965427425836507221875}{12762048097087747113660585463702347776}\cdot t^7+\frac{3401873847388167134323386036657346883740726809147654923671875}{12762048097087747113660585463702347776}\cdot t^5-\frac{954077636660051060642790085905294487121185045100059358109375}{25524096194175494227321170927404695552}\cdot t^3+\frac{44413680621159976539385273459102846501782297153697236703125}{25524096194175494227321170927404695552}\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.