Rule: Q[1, 2, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^3-3\cdot t$
• $P_3$:
  $2\cdot t^{13}-\frac{629}{8}\cdot t^{11}+\frac{17435}{16}\cdot t^9-\frac{105435}{16}\cdot t^7+\frac{557865}{32}\cdot t^5-\frac{2248785}{128}\cdot t^3+\frac{1133055}{256}\cdot t$
• $P_4$:
  $2\cdot t^{33}-\frac{3868363632647762340929349819043}{10049566913423152616959022136}\cdot t^{31}+\frac{8430026763398522960166747363195775}{261288739749001968040934575536}\cdot t^{29}-\frac{5693552740397442351951872612613544795}{3658042356486027552573084057504}\cdot t^{27}+\frac{117392946727225262907783260017500713685}{2438694904324018368382056038336}\cdot t^{25}-\frac{4909232891777820073049782510579590086655}{4877389808648036736764112076672}\cdot t^{23}+\frac{142672155640543737221615785127867356682415}{9754779617296073473528224153344}\cdot t^{21}-\frac{416814309165456309181813912986235084703475}{2787079890656020992436635472384}\cdot t^{19}+\frac{6008630303490478509874493928882027275380575}{5574159781312041984873270944768}\cdot t^{17}-\frac{60603219722255771330292820339073608766069175}{11148319562624083969746541889536}\cdot t^{15}+\frac{32346812700406633522862432330061087692360475}{1715126086557551379961006444544}\cdot t^{13}-\frac{150132604097588143758417392423343076769461425}{3430252173115102759922012889088}\cdot t^{11}+\frac{40584555899455401993657516550893544133046375}{623682213293655047258547798016}\cdot t^9-\frac{72460347750105257840049530972187649118992125}{1247364426587310094517095596032}\cdot t^7+\frac{70489255901535674454493913527506678610924125}{2494728853174620189034191192064}\cdot t^5-\frac{32179665974723661869792522467500363649815375}{4989457706349240378068382384128}\cdot t^3+\frac{5000311452788290134073272393910186207099875}{9978915412698480756136764768256}\cdot t$

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.