Rule: Q[16, 27]

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.

• $P_1$:
  $t^{16}-120\cdot t^{14}+5460\cdot t^{12}-120120\cdot t^{10}+1351350\cdot t^8-7567560\cdot t^6+18918900\cdot t^4-16216200\cdot t^2+2027025$
• $P_2$:
  $t^{43}-\frac{14209476191}{13835649}\cdot t^{41}+\frac{98792931897166}{235206033}\cdot t^{39}-\frac{67724098150786454}{705618099}\cdot t^{37}+\frac{3304758489709544465}{235206033}\cdot t^{35}-\frac{332883023606592313855}{235206033}\cdot t^{33}+\frac{24054477667866677591560}{235206033}\cdot t^{31}-\frac{426386128007909457908520}{78402011}\cdot t^{29}+\frac{16944703642967175728362710}{78402011}\cdot t^{27}-\frac{507440090041357104905323050}{78402011}\cdot t^{25}+\frac{675543100708029451451053500}{4611883}\cdot t^{23}-\frac{196060074777196411370683594500}{78402011}\cdot t^{21}+\frac{2508946561255329365297626248750}{78402011}\cdot t^{19}-\frac{23799914344439114631036768731250}{78402011}\cdot t^{17}+\frac{9681426005297545461141994815000}{4611883}\cdot t^{15}-\frac{47661682150715268731755444785000}{4611883}\cdot t^{13}+\frac{161560763746224820795764841269375}{4611883}\cdot t^{11}-\frac{359617302987958212288824978870625}{4611883}\cdot t^9+\frac{490135166984052481165646117996250}{4611883}\cdot t^7-\frac{366299179065911333304776407443750}{4611883}\cdot t^5+\frac{123119907398763238284686924934375}{4611883}\cdot t^3-\frac{11692695166596478222344146615625}{4611883}\cdot t$

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.