Rule: Q[1, 2, 44]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{47}-\frac{3514153654452277745561}{3361510671905005977}\cdot t^{45}+\frac{560094854974915264947525}{1120503557301668659}\cdot t^{43}-\frac{23235237349503802180731855}{160071936757381237}\cdot t^{41}+\frac{4589211166692680833587627675}{160071936757381237}\cdot t^{39}-\frac{654332443892435585022558356115}{160071936757381237}\cdot t^{37}+\frac{69768361009792761626324762278245}{160071936757381237}\cdot t^{35}-\frac{5686994763539639731787371497356625}{160071936757381237}\cdot t^{33}+\frac{359282803522295051872251121270120050}{160071936757381237}\cdot t^{31}-\frac{17733237553633650541404345725259647250}{160071936757381237}\cdot t^{29}+\frac{686283328499784836818007437506794865150}{160071936757381237}\cdot t^{27}-\frac{20823783775003386821900404721580442384950}{160071936757381237}\cdot t^{25}+\frac{493722260787840982633382484795192579093750}{160071936757381237}\cdot t^{23}-\frac{9085617813980855043382421341720857456663750}{160071936757381237}\cdot t^{21}+\frac{128439612904821302909650599497952197726006250}{160071936757381237}\cdot t^{19}-\frac{1374782528039199493921639619119043483063441250}{160071936757381237}\cdot t^{17}+\frac{10925504486189207144722730433672171252428495625}{160071936757381237}\cdot t^{15}-\frac{62786031519102820709806472412200567904462515625}{160071936757381237}\cdot t^{13}+\frac{251727692309709392180155564004512495180539909375}{160071936757381237}\cdot t^{11}-\frac{669791682913080396700696637662556444875218796875}{160071936757381237}\cdot t^9+\frac{1099616293294393121499592062088006516136395509375}{160071936757381237}\cdot t^7-\frac{993607557345241528937930176383411431497397184375}{160071936757381237}\cdot t^5+\frac{403454009725495425625576495763098339481090390625}{160071936757381237}\cdot t^3-\frac{46339333129265119198494450887799679578225328125}{160071936757381237}\cdot t$

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.