Rule: Q[4, 10, 23]

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.

• $P_1$:
  $t^4-6\cdot t^2+3$
• $P_2$:
  $t^{14}-\frac{477}{7}\cdot t^{12}+\frac{11241}{7}\cdot t^{10}-\frac{112815}{7}\cdot t^8+68715\cdot t^6-108945\cdot t^4+46845\cdot t^2-2835$
• $P_3$:
  $t^{37}-\frac{6226182996938848703671947830267937459}{9317405211111424789646489158029125}\cdot t^{35}+\frac{1701569291963629280644285373462088586314}{9317405211111424789646489158029125}\cdot t^{33}-\frac{258921363264247493928437277716237672558172}{9317405211111424789646489158029125}\cdot t^{31}+\frac{64550863379083319227901606179277777991378984}{24225253548889704453080871810875725}\cdot t^{29}-\frac{2237403230307982824204075877211952093325520472}{13044367295555994705505084821240775}\cdot t^{27}+\frac{1301824950326976875322138441601756371669444509892}{169576774842227931171566102676130075}\cdot t^{25}-\frac{41293931112551612462680410155624348980525323604692}{169576774842227931171566102676130075}\cdot t^{23}+\frac{605169555288450519382885973313343549650650322258}{109616531895428526937017519506225}\cdot t^{21}-\frac{433601256383989459287846970930926638450697535220478}{4845050709777940890616174362175145}\cdot t^{19}+\frac{4991981906330563494448299725330181345523890509862096}{4845050709777940890616174362175145}\cdot t^{17}-\frac{338290227103599079848570712355177937242680365698556}{40714711846873452862320792959455}\cdot t^{15}+\frac{214529596760313530496117411501691319100625361400192}{4672180048001871639938451651085}\cdot t^{13}-\frac{3691770165235902081097018470979844213185024069244112}{21923306379085705387403503901245}\cdot t^{11}+\frac{1715501667182893427870462777457673216139529754905876}{4384661275817141077480700780249}\cdot t^9-\frac{336302133329431666289465328000456015231649574072556}{626380182259591582497242968607}\cdot t^7+\frac{241928371312403394361155293027901613139704049285979}{626380182259591582497242968607}\cdot t^5-\frac{71011801504343804759464408169161466973021180635709}{626380182259591582497242968607}\cdot t^3+\frac{3980015100000250097438378837886072145509678545682}{626380182259591582497242968607}\cdot t$

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.