Rule: Q[12, 19]

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.

• $P_1$:
  $4096\cdot t^{12}-135168\cdot t^{10}+1520640\cdot t^8-7096320\cdot t^6+13305600\cdot t^4-7983360\cdot t^2+665280$
• $P_2$:
  $4096\cdot t^{31}-\frac{4334433435648}{6191363}\cdot t^{29}+\frac{319811495107584}{6191363}\cdot t^{27}-\frac{13444953069874176}{6191363}\cdot t^{25}+\frac{358121780669664000}{6191363}\cdot t^{23}-\frac{6360369496467356160}{6191363}\cdot t^{21}+\frac{77223623463557645760}{6191363}\cdot t^{19}-\frac{646849907001518633280}{6191363}\cdot t^{17}+\frac{3727916093739283099920}{6191363}\cdot t^{15}-\frac{14582322240678352641600}{6191363}\cdot t^{13}+\frac{37731353609884310075700}{6191363}\cdot t^{11}-\frac{61942301424108198393300}{6191363}\cdot t^9+\frac{60404032344599956037025}{6191363}\cdot t^7-\frac{31398027243597292127850}{6191363}\cdot t^5+\frac{28569575948565113587125}{24765452}\cdot t^3-\frac{1806968329133745652875}{24765452}\cdot t$

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.