Rule: Q[6, 32]

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.

• $P_1$:
  $t^6-15\cdot t^4+45\cdot t^2-15$
• $P_2$:
  $t^{38}-\frac{426508646085454018340044123}{700595787372387283311781}\cdot t^{36}+\frac{346683113024500619340181725035}{2101787362117161849935343}\cdot t^{34}-\frac{239869565992784539479089913889735}{9107745235841034683053153}\cdot t^{32}+\frac{3599061977049624789516729067425660}{1301106462263004954721879}\cdot t^{30}-\frac{1840261866257062232371781870766366460}{9107745235841034683053153}\cdot t^{28}+\frac{13772391545298501179996552794258949340}{1301106462263004954721879}\cdot t^{26}-\frac{40470872452775648393467715394678670500}{100085112481769611901683}\cdot t^{24}+\frac{1135542409180436883959957333179596404250}{100085112481769611901683}\cdot t^{22}-\frac{2127537122479900573648745363502920447250}{9098646589251782900153}\cdot t^{20}+\frac{32007649316364586639460310146453905809750}{9098646589251782900153}\cdot t^{18}-\frac{347180456952427323458645302429820408699250}{9098646589251782900153}\cdot t^{16}+\frac{2663214120190447439675499171201971818192500}{9098646589251782900153}\cdot t^{14}-\frac{14051945959824318267618994559937552262867500}{9098646589251782900153}\cdot t^{12}+\frac{329035230890205330745434573414957374302500}{61064742209743509397}\cdot t^{10}-\frac{106831146310537688550892586998844414338657500}{9098646589251782900153}\cdot t^8+\frac{133231971690197589573051168691884520603850625}{9098646589251782900153}\cdot t^6-\frac{82029198926422262900053390708781415481809375}{9098646589251782900153}\cdot t^4+\frac{18501201902498849290951060686243859083403125}{9098646589251782900153}\cdot t^2-\frac{615962444143380278091548235801288166884375}{9098646589251782900153}$

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.