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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{15}-\frac{443040}{191}\cdot t^{13}+\frac{5766480}{191}\cdot t^{11}-\frac{34180440}{191}\cdot t^9+\frac{97309620}{191}\cdot t^7-\frac{129077550}{191}\cdot t^5+\frac{68923575}{191}\cdot t^3-\frac{18129825}{382}\cdot t$
• $P_3$:
  $64\cdot t^{29}-\frac{187328470189621764699453638239840}{20786051549784625378492529277}\cdot t^{27}+\frac{1255248598475034717191980792235504}{2309561283309402819832503253}\cdot t^{25}-\frac{42784394363125384161177822410764680}{2309561283309402819832503253}\cdot t^{23}+\frac{8246118673784779029369136814255613380}{20786051549784625378492529277}\cdot t^{21}-\frac{38897445323606839222495575182426277890}{6928683849928208459497509759}\cdot t^{19}+\frac{372477999616173391003825685695228903775}{6928683849928208459497509759}\cdot t^{17}-\frac{14584240008950923529222835020228384649275}{41572103099569250756985058554}\cdot t^{15}+\frac{10744593388020327801084647828771530211425}{6928683849928208459497509759}\cdot t^{13}-\frac{10524838535744497451204354912261922979225}{2309561283309402819832503253}\cdot t^{11}+\frac{59653685161839252474132665315537646101200}{6928683849928208459497509759}\cdot t^9-\frac{22900068516000015377348569889074116547875}{2309561283309402819832503253}\cdot t^7+\frac{472986231349200693101011300856062411063125}{73905961065900890234640104096}\cdot t^5-\frac{295071385324867457196440909017710896719875}{147811922131801780469280208192}\cdot t^3+\frac{3809360119828670247345583114017824968125}{18476490266475222558660026024}\cdot t$

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.