Rule: Q[18, 29]

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.

• $P_1$:
  $t^{18}-153\cdot t^{16}+9180\cdot t^{14}-278460\cdot t^{12}+4594590\cdot t^{10}-41351310\cdot t^8+192972780\cdot t^6-413513100\cdot t^4+310134825\cdot t^2-34459425$
• $P_2$:
  $t^{47}-\frac{30526986556787057986094911}{34536388190176557658117}\cdot t^{45}+\frac{12138564322035279957243164895}{34536388190176557658117}\cdot t^{43}-\frac{2887667945631719484276085402905}{34536388190176557658117}\cdot t^{41}+\frac{460823145246047544555370390839315}{34536388190176557658117}\cdot t^{39}-\frac{52410302531123351991000599400833025}{34536388190176557658117}\cdot t^{37}+\frac{4404399472255420987489877975256625425}{34536388190176557658117}\cdot t^{35}-\frac{14725754067833089704677909788599190725}{1817704641588239876743}\cdot t^{33}+\frac{13630577573329822860862283859402828558450}{34536388190176557658117}\cdot t^{31}-\frac{513680614585164892577367671203039655553750}{34536388190176557658117}\cdot t^{29}+\frac{15039040754220639345945698414019292353158550}{34536388190176557658117}\cdot t^{27}-\frac{342265408367984016610523948998592429328262650}{34536388190176557658117}\cdot t^{25}+\frac{6038768791821251031028524834538249825514943750}{34536388190176557658117}\cdot t^{23}-\frac{82105613018299882894821303525128753255562341250}{34536388190176557658117}\cdot t^{21}+\frac{852106871934456226233340174689697073070135401250}{34536388190176557658117}\cdot t^{19}-\frac{18445093884818217100328081258150033286921288750}{95668665346749467197}\cdot t^{17}+\frac{2023827988851143029014475652479094414219694511875}{1817704641588239876743}\cdot t^{15}-\frac{8420351328583407300863631651917165790856250765625}{1817704641588239876743}\cdot t^{13}+\frac{24378577682871610020076939467639284190688165865625}{1817704641588239876743}\cdot t^{11}-\frac{46770619343749748736243484345523735856820175559375}{1817704641588239876743}\cdot t^9+\frac{55320492496032159931706082408097641358419554578125}{1817704641588239876743}\cdot t^7-\frac{35973100298760930489856292995027013720579954109375}{1817704641588239876743}\cdot t^5+\frac{10494560168710566235527817684196730065104163859375}{1817704641588239876743}\cdot t^3-\frac{877327576992538328297354672389431885255636890625}{1817704641588239876743}\cdot t$

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.