Rule: Q[1, 2, 42]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^3-3\cdot t$
• $P_3$:
  $t^{45}-\frac{762527411580585593007}{800788896593667320}\cdot t^{43}+\frac{330621627713348403455121}{800788896593667320}\cdot t^{41}-\frac{8663631528680372585580561}{80078889659366732}\cdot t^{39}+\frac{1535772869449538402062592667}{80078889659366732}\cdot t^{37}-\frac{390704370723420465296997339291}{160157779318733464}\cdot t^{35}+\frac{36917652528360486778214899215909}{160157779318733464}\cdot t^{33}-\frac{330852861051256758479359872977199}{20019722414841683}\cdot t^{31}+\frac{18229453024076752829950312788309255}{20019722414841683}\cdot t^{29}-\frac{3108711955918656830557715636305084515}{80078889659366732}\cdot t^{27}+\frac{102773515632197187781378336592581435485}{80078889659366732}\cdot t^{25}-\frac{1314971476522493465593375286602560061275}{40039444829683366}\cdot t^{23}+\frac{25900578182441782978707719481374119881825}{40039444829683366}\cdot t^{21}-\frac{777877942203416774175780477037583950626375}{80078889659366732}\cdot t^{19}+\frac{8781680252601220464036986745916532717429625}{80078889659366732}\cdot t^{17}-\frac{18274177354789032174786779469600124085958375}{20019722414841683}\cdot t^{15}+\frac{109221084024162892891526302692993204456438000}{20019722414841683}\cdot t^{13}-\frac{3616185682017306092521939048990765354684416375}{160157779318733464}\cdot t^{11}+\frac{9849018371448012774440664422186942602336295625}{160157779318733464}\cdot t^9-\frac{8193392045325085515324066921275675746129670625}{80078889659366732}\cdot t^7+\frac{7408941862531761611815879609450855109811466875}{80078889659366732}\cdot t^5-\frac{5918878169021127078610941858630714939225504375}{160157779318733464}\cdot t^3+\frac{652039258754883799125597180996577436696375625}{160157779318733464}\cdot t$

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.