Rule: Q[16, 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.

• $P_1$:
  $t^{16}-120\cdot t^{14}+5460\cdot t^{12}-120120\cdot t^{10}+1351350\cdot t^8-7567560\cdot t^6+18918900\cdot t^4-16216200\cdot t^2+2027025$
• $P_2$:
  $t^{41}-\frac{248054953244}{408408193}\cdot t^{39}+\frac{202411153785854}{1225224579}\cdot t^{37}-\frac{10896701130176420}{408408193}\cdot t^{35}+\frac{1168326885794833765}{408408193}\cdot t^{33}-\frac{88100064328183027120}{408408193}\cdot t^{31}+\frac{4829881900863762582840}{408408193}\cdot t^{29}-\frac{196305899121812340740880}{408408193}\cdot t^{27}+\frac{5979351243855464607582450}{408408193}\cdot t^{25}-\frac{137094302135218919287797000}{408408193}\cdot t^{23}+\frac{2364173128625785876032133500}{408408193}\cdot t^{21}-\frac{30492012440248769076541875000}{408408193}\cdot t^{19}+\frac{291021402143092545730877321250}{408408193}\cdot t^{17}-\frac{2022098444553556847182174470000}{408408193}\cdot t^{15}+\frac{9991374953853472107355221795000}{408408193}\cdot t^{13}-\frac{33962761969004744357650057890000}{408408193}\cdot t^{11}+\frac{75753940895289273032147104498125}{408408193}\cdot t^9-\frac{103398360408377630918290145677500}{408408193}\cdot t^7+\frac{77345027955580891543033953206250}{408408193}\cdot t^5-\frac{26007998459469469863402845362500}{408408193}\cdot t^3+\frac{2470336694583616570015044365625}{408408193}\cdot t$

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.