Rule: Q[2, 3, 4, 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.

• $P_1$:
  $t^2-1$
• $P_2$:
  $t^5-7\cdot t^3+6\cdot t$
• $P_3$:
  $t^9-\frac{71}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{9}\cdot t^3+\frac{590}{3}\cdot t$
• $P_4$:
  $t^{27}-\frac{8054880965040595537504108712022329}{2616420482506284892722222867462}\cdot t^{25}+\frac{38318532686490862474726678493408987389}{54944830132631982747166680216702}\cdot t^{23}-\frac{3709235259758805845518111914465376906699}{54944830132631982747166680216702}\cdot t^{21}+\frac{65453924789021995893651495904258813923893}{18314943377543994249055560072234}\cdot t^{19}-\frac{346045948455444559426569734061408230412088}{3052490562923999041509260012039}\cdot t^{17}+\frac{6823477816157005987362812950159827283444729}{3052490562923999041509260012039}\cdot t^{15}-\frac{12043632963166837691018952653624243452039725}{436070080417714148787037144577}\cdot t^{13}+\frac{92084416354677522990744585382536526442292570}{436070080417714148787037144577}\cdot t^{11}-\frac{844353751622751312357970658347724980970739555}{872140160835428297574074289154}\cdot t^9+\frac{2195390217545643743067297557248776952554001455}{872140160835428297574074289154}\cdot t^7-\frac{2933303286161246373455525132291856194622316065}{872140160835428297574074289154}\cdot t^5+\frac{1644110385427518271189164617717505558924272025}{872140160835428297574074289154}\cdot t^3-\frac{111889442686943409393747161516766198799180725}{436070080417714148787037144577}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (probabilists') type can be downloaded here packed into a single file.