Rule: Q[2, 7, 18]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^9-\frac{346}{5}\cdot t^7+\frac{1743}{5}\cdot t^5-\frac{1113}{2}\cdot t^3+\frac{399}{2}\cdot t$
• $P_3$:
  $4\cdot t^{27}-\frac{23713059798960210194599}{40133743389473733395}\cdot t^{25}+\frac{38490928736959356647640159}{1043477328126317068270}\cdot t^{23}-\frac{2669596356929556607160822889}{2086954656252634136540}\cdot t^{21}+\frac{1251302066060699168832390282579}{45913002437557951003880}\cdot t^{19}-\frac{8560045570713565284471721748121}{22956501218778975501940}\cdot t^{17}+\frac{305729943623714833393266252893961}{91826004875115902007760}\cdot t^{15}-\frac{54678536972190494062088435867835}{2825415534618950831008}\cdot t^{13}+\frac{50763533942882437096743705288123}{706353883654737707752}\cdot t^{11}-\frac{337716694675472793580850976022851}{2054847661541055149824}\cdot t^9+\frac{893850191374390231079302957672731}{4109695323082110299648}\cdot t^7-\frac{1231431587235049993945122648792933}{8219390646164220599296}\cdot t^5+\frac{723505001219868112063866791914905}{16438781292328441198592}\cdot t^3-\frac{56456117968234496017092998491395}{16438781292328441198592}\cdot t$

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.