Rule: Q[2, 5, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^7-\frac{106}{3}\cdot t^5+\frac{215}{3}\cdot t^3-\frac{55}{2}\cdot t$
• $P_3$:
  $4\cdot t^{23}-\frac{190561781511590}{454088400077}\cdot t^{21}+\frac{73610338759101533}{4086795600693}\cdot t^{19}-\frac{50596907879744273137}{122603868020790}\cdot t^{17}+\frac{677980562013908772311}{122603868020790}\cdot t^{15}-\frac{56215914325076525467}{1257475569444}\cdot t^{13}+\frac{547119670729843344497}{2514951138888}\cdot t^{11}-\frac{3112387970240841410195}{5029902277776}\cdot t^9+\frac{2167197645791877595589}{2235512123456}\cdot t^7-\frac{3377729383397684509579}{4471024246912}\cdot t^5+\frac{2188577584705176879445}{8942048493824}\cdot t^3-\frac{396238218708225835095}{17884096987648}\cdot t$

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.