Rule: Q[1, 2, 68]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{71}-\frac{682318202587104478637369101538978335987}{281883215233401101190419706483682719}\cdot t^{69}+\frac{259685236589810023339269185894208000066269}{93961071744467033730139902161227573}\cdot t^{67}-\frac{16923131749860167100598912556807256541028607}{8541915613133366702739991105566143}\cdot t^{65}+\frac{8552623377065592571482730622525340080360939320}{8541915613133366702739991105566143}\cdot t^{63}-\frac{3244018246186042656705462835078560180216563371800}{8541915613133366702739991105566143}\cdot t^{61}+\frac{959951449393530780771880182144610370138463872788440}{8541915613133366702739991105566143}\cdot t^{59}-\frac{227435245423035005883763525071276380538129813470193240}{8541915613133366702739991105566143}\cdot t^{57}+\frac{43936070421289529119452067241430568050466812513888008820}{8541915613133366702739991105566143}\cdot t^{55}-\frac{7012303547812789803240396353138347200290159994677956932900}{8541915613133366702739991105566143}\cdot t^{53}+\frac{933616424608344846184071582056521662636504178404973274166900}{8541915613133366702739991105566143}\cdot t^{51}-\frac{104426837356210113935369190634498938942555090424339836890884500}{8541915613133366702739991105566143}\cdot t^{49}+\frac{9862626280470574283086930075456120964883416169379570702690257000}{8541915613133366702739991105566143}\cdot t^{47}-\frac{789248286348861119226830885053737302490888045294224478359216421000}{8541915613133366702739991105566143}\cdot t^{45}+\frac{53628389403971875367482556504564901487400412832774809355242552405000}{8541915613133366702739991105566143}\cdot t^{43}-\frac{3097028129251112009696280725475854442379299296248573441996019005365000}{8541915613133366702739991105566143}\cdot t^{41}+\frac{151988394839634752516343216905566218029876054173160297241329863242386250}{8541915613133366702739991105566143}\cdot t^{39}-\frac{6331369803462715339470133326658630461933496905027274902061737680748461250}{8541915613133366702739991105566143}\cdot t^{37}+\frac{223399846555166463959579161590391065963954548779927997489889714227356496250}{8541915613133366702739991105566143}\cdot t^{35}-\frac{6655826904074548100708643005588190467244209404417834739162084467835624006250}{8541915613133366702739991105566143}\cdot t^{33}+\frac{166734776867317465197570589102326832240925938014571727671379763528914850525000}{8541915613133366702739991105566143}\cdot t^{31}-\frac{3493162448199337626163873634693491800389105128805636546496639578797175747025000}{8541915613133366702739991105566143}\cdot t^{29}+\frac{60795557450030824559950263424599869094092235538144411090434875629925554562025000}{8541915613133366702739991105566143}\cdot t^{27}-\frac{871798382243441199110203344157884655697451917323174393647482409906126358992825000}{8541915613133366702739991105566143}\cdot t^{25}+\frac{10197546151216019423112397483276163103291529088574637942957363863901055903477812500}{8541915613133366702739991105566143}\cdot t^{23}-\frac{96115838746816921436354202025537132264892881211369111169050519752232387073798562500}{8541915613133366702739991105566143}\cdot t^{21}+\frac{719108738196108558664242219971811297082302018836007928254931869706733790958628812500}{8541915613133366702739991105566143}\cdot t^{19}-\frac{4192015855614817172169462144234056458722971776623244609632834787933920013367551312500}{8541915613133366702739991105566143}\cdot t^{17}+\frac{18601285222416027344069990634378924745919958964908608510114871852760459703224107375000}{8541915613133366702739991105566143}\cdot t^{15}-\frac{60977303804958930498216287574489841472223302639757001248668184387358528650331426875000}{8541915613133366702739991105566143}\cdot t^{13}+\frac{141973329243732112213789955967159366840521560022596747070269041027933124878958546875000}{8541915613133366702739991105566143}\cdot t^{11}-\frac{222493928151658234911998904297918807159014171774206161263549811150979810957678906875000}{8541915613133366702739991105566143}\cdot t^9+\frac{217237152955556046512376453203608096002708611446861484618054916586370313303630440859375}{8541915613133366702739991105566143}\cdot t^7-\frac{117198223380316004658298088500400248878243996139471569518392188126838034087191343671875}{8541915613133366702739991105566143}\cdot t^5+\frac{28280771221338496708447133010255315596321059757763212221343415045076057668256590234375}{8541915613133366702739991105566143}\cdot t^3-\frac{1893555149364347217457371831159728500253929669243317821514530273437289698914793359375}{8541915613133366702739991105566143}\cdot t$

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.