Rule: Q[6, 9, 14]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{15}-\frac{13845}{191}\cdot t^{13}+\frac{360405}{191}\cdot t^{11}-\frac{4272555}{191}\cdot t^9+\frac{24327405}{191}\cdot t^7-\frac{64538775}{191}\cdot t^5+\frac{68923575}{191}\cdot t^3-\frac{18129825}{191}\cdot t$
• $P_3$:
  $t^{29}-\frac{5854014693425680146857926194995}{20786051549784625378492529277}\cdot t^{27}+\frac{78453037404689669824498799514719}{2309561283309402819832503253}\cdot t^{25}-\frac{5348049295390673020147227801345585}{2309561283309402819832503253}\cdot t^{23}+\frac{2061529668446194757342284203563903345}{20786051549784625378492529277}\cdot t^{21}-\frac{19448722661803419611247787591213138945}{6928683849928208459497509759}\cdot t^{19}+\frac{372477999616173391003825685695228903775}{6928683849928208459497509759}\cdot t^{17}-\frac{14584240008950923529222835020228384649275}{20786051549784625378492529277}\cdot t^{15}+\frac{42978373552081311204338591315086120845700}{6928683849928208459497509759}\cdot t^{13}-\frac{84198708285955979609634839298095383833800}{2309561283309402819832503253}\cdot t^{11}+\frac{954458962589428039586122645048602337619200}{6928683849928208459497509759}\cdot t^9-\frac{732802192512000492075154236450371729532000}{2309561283309402819832503253}\cdot t^7+\frac{945972462698401386202022601712124822126250}{2309561283309402819832503253}\cdot t^5-\frac{590142770649734914392881818035421793439750}{2309561283309402819832503253}\cdot t^3+\frac{121899523834517447915058659648570398980000}{2309561283309402819832503253}\cdot t$

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.