Rule: Q[1, 10, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{11}-55\cdot t^9+495\cdot t^7-\frac{3465}{2}\cdot t^5+\frac{17325}{8}\cdot t^3-\frac{10395}{16}\cdot t$
• $P_3$:
  $2\cdot t^{29}-\frac{12380943233}{40529468}\cdot t^{27}+\frac{1615566477339}{81058936}\cdot t^{25}-\frac{59326255051605}{81058936}\cdot t^{23}+\frac{2721315373896825}{162117872}\cdot t^{21}-\frac{23381025270609285}{92638784}\cdot t^{19}+\frac{470995616550501135}{185277568}\cdot t^{17}-\frac{1596425847858783945}{92638784}\cdot t^{15}+\frac{7219583943976289925}{92638784}\cdot t^{13}-\frac{340758017553554982225}{1482220544}\cdot t^{11}+\frac{1260875025129864476475}{2964441088}\cdot t^9-\frac{1371849782210823447675}{2964441088}\cdot t^7+\frac{224891447290917875325}{846983168}\cdot t^5-\frac{221182651456612399125}{3387932672}\cdot t^3+\frac{28114295564123715375}{6775865344}\cdot t$

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.