Rule: Q[3, 10, 20]

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.

• $P_1$:
  $t^3-3\cdot t$
• $P_2$:
  $t^{13}-\frac{629}{8}\cdot t^{11}+\frac{17435}{8}\cdot t^9-\frac{105435}{4}\cdot t^7+\frac{557865}{4}\cdot t^5-\frac{2248785}{8}\cdot t^3+\frac{1133055}{8}\cdot t$
• $P_3$:
  $t^{33}-\frac{3868363632647762340929349819043}{10049566913423152616959022136}\cdot t^{31}+\frac{8430026763398522960166747363195775}{130644369874500984020467287768}\cdot t^{29}-\frac{5693552740397442351951872612613544795}{914510589121506888143271014376}\cdot t^{27}+\frac{117392946727225262907783260017500713685}{304836863040502296047757004792}\cdot t^{25}-\frac{4909232891777820073049782510579590086655}{304836863040502296047757004792}\cdot t^{23}+\frac{142672155640543737221615785127867356682415}{304836863040502296047757004792}\cdot t^{21}-\frac{416814309165456309181813912986235084703475}{43548123291500328006822429256}\cdot t^{19}+\frac{6008630303490478509874493928882027275380575}{43548123291500328006822429256}\cdot t^{17}-\frac{60603219722255771330292820339073608766069175}{43548123291500328006822429256}\cdot t^{15}+\frac{32346812700406633522862432330061087692360475}{3349855637807717538986340712}\cdot t^{13}-\frac{150132604097588143758417392423343076769461425}{3349855637807717538986340712}\cdot t^{11}+\frac{40584555899455401993657516550893544133046375}{304532330709792503544212792}\cdot t^9-\frac{72460347750105257840049530972187649118992125}{304532330709792503544212792}\cdot t^7+\frac{70489255901535674454493913527506678610924125}{304532330709792503544212792}\cdot t^5-\frac{32179665974723661869792522467500363649815375}{304532330709792503544212792}\cdot t^3+\frac{5000311452788290134073272393910186207099875}{304532330709792503544212792}\cdot t$

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.