Rule: Q[4, 27]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{31}-\frac{6935573019906972}{2131629896939}\cdot t^{29}+\frac{14028659586556851864}{49027487629597}\cdot t^{27}-\frac{703432775795215778325}{49027487629597}\cdot t^{25}+\frac{22329286500781131063075}{49027487629597}\cdot t^{23}-\frac{81958994450919132378975}{8526519587756}\cdot t^{21}+\frac{293986041775374683559825}{2131629896939}\cdot t^{19}-\frac{46137771541636426411434675}{34106078351024}\cdot t^{17}+\frac{307091726299187887869937125}{34106078351024}\cdot t^{15}-\frac{5439345752883001170870784125}{136424313404096}\cdot t^{13}+\frac{7745935158254298069970030125}{68212156702048}\cdot t^{11}-\frac{107806127340207725167962848625}{545697253616384}\cdot t^9+\frac{106195135331703505454470978875}{545697253616384}\cdot t^7-\frac{212700560299676707590815608125}{2182789014465536}\cdot t^5+\frac{5860305021723339953159769375}{272848626808192}\cdot t^3-\frac{14114684606831488089300515625}{8731156057862144}\cdot t$

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.