Rule: Q[12, 25]

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.

• $P_1$:
  $t^{12}-66\cdot t^{10}+1485\cdot t^8-13860\cdot t^6+51975\cdot t^4-62370\cdot t^2+10395$
• $P_2$:
  $t^{37}-\frac{2242882561968}{4258858723}\cdot t^{35}+\frac{8939123100043785}{72400598291}\cdot t^{33}-\frac{1236158268592187160}{72400598291}\cdot t^{31}+\frac{112633308964622075850}{72400598291}\cdot t^{29}-\frac{50081627138100920708940}{506804188037}\cdot t^{27}+\frac{29751136061177905715298870}{6588454444481}\cdot t^{25}-\frac{994935787105269473595648000}{6588454444481}\cdot t^{23}+\frac{3504700705746196080352899000}{941207777783}\cdot t^{21}-\frac{63714067370241571654509847500}{941207777783}\cdot t^{19}+\frac{848112169521766272861276643500}{941207777783}\cdot t^{17}-\frac{479527219107833500642357143000}{55365163399}\cdot t^{15}+\frac{3255793892271702277374179688750}{55365163399}\cdot t^{13}-\frac{28362746464693530482639227500}{103874603}\cdot t^{11}+\frac{3522730714418601001673686518750}{4258858723}\cdot t^9-\frac{927140199102168631425567810000}{608408389}\cdot t^7+\frac{929037777119335903616440531875}{608408389}\cdot t^5-\frac{414606244223549817550807987500}{608408389}\cdot t^3+\frac{52070220494912921376023128125}{608408389}\cdot t$

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.