Rule: Q[6, 9, 16]

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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{15}-\frac{443040}{191}\cdot t^{13}+\frac{5766480}{191}\cdot t^{11}-\frac{34180440}{191}\cdot t^9+\frac{97309620}{191}\cdot t^7-\frac{129077550}{191}\cdot t^5+\frac{68923575}{191}\cdot t^3-\frac{18129825}{382}\cdot t$
• $P_3$:
  $64\cdot t^{31}-\frac{1824323754501142631098863532500221108960}{127678172195960946379309627115979517}\cdot t^{29}+\frac{164127716959105517589673680303217944307120}{127678172195960946379309627115979517}\cdot t^{27}-\frac{24216086299404409078777124405117714234420920}{383034516587882839137928881347938551}\cdot t^{25}+\frac{734965092199631214437839217619863065211165900}{383034516587882839137928881347938551}\cdot t^{23}-\frac{14626520347829850321478887895851467434568457250}{383034516587882839137928881347938551}\cdot t^{21}+\frac{197042092115289485868836481827746087311830959525}{383034516587882839137928881347938551}\cdot t^{19}-\frac{3646561598011138324056834849627177832302053512075}{766069033175765678275857762695877102}\cdot t^{17}+\frac{46446025834352566579721941475075622655427691161125}{1532138066351531356551715525391754204}\cdot t^{15}-\frac{134489432478225917549691005099173615145785246235125}{1021425377567687571034477016927836136}\cdot t^{13}+\frac{780492772593427554317977809703175091245115100816625}{2042850755135375142068954033855672272}\cdot t^{11}-\frac{265690651878126795786194982639169187580326050571125}{371427410024613662194355278882849504}\cdot t^9+\frac{608079922581907564869728793471397218483337468364625}{742854820049227324388710557765699008}\cdot t^7-\frac{781520970338406505246184963233696013614138600216875}{1485709640098454648777421115531398016}\cdot t^5+\frac{486096311613285833355945554098452142978708378284375}{2971419280196909297554842231062796032}\cdot t^3-\frac{100252484253233875494515769323786003044777611875625}{5942838560393818595109684462125592064}\cdot t$

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.