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.

• $P_1$:
  $262144\cdot t^{18}-20054016\cdot t^{16}+601620480\cdot t^{14}-9124577280\cdot t^{12}+75277762560\cdot t^{10}-338749931520\cdot t^8+790416506880\cdot t^6-846874828800\cdot t^4+317578060800\cdot t^2-17643225600$
• $P_2$:
  $262144\cdot t^{47}-\frac{4001233181971193264353432174592}{34536388190176557658117}\cdot t^{45}+\frac{795512951408904107277888054558720}{34536388190176557658117}\cdot t^{43}-\frac{94623103242460184060758766482391040}{34536388190176557658117}\cdot t^{41}+\frac{7550126411711242969995188483511336960}{34536388190176557658117}\cdot t^{39}-\frac{429345198334962499510276910291624140800}{34536388190176557658117}\cdot t^{37}+\frac{18040420238358204364758540186651137740800}{34536388190176557658117}\cdot t^{35}-\frac{30158344330922167715180359247051142604800}{1817704641588239876743}\cdot t^{33}+\frac{13957711435089738609522978672028496443852800}{34536388190176557658117}\cdot t^{31}-\frac{263004474667604424999612247655956303643520000}{34536388190176557658117}\cdot t^{29}+\frac{3849994433080483672562098793988938842408588800}{34536388190176557658117}\cdot t^{27}-\frac{43809972271101954126147065471819830954017619200}{34536388190176557658117}\cdot t^{25}+\frac{386481202676560065985825589410447988832956400000}{34536388190176557658117}\cdot t^{23}-\frac{2627379616585596252634281712804120104177994920000}{34536388190176557658117}\cdot t^{21}+\frac{13633709950951299619733442795035153169122166420000}{34536388190176557658117}\cdot t^{19}-\frac{147560751078545736802624650065200266295370310000}{95668665346749467197}\cdot t^{17}+\frac{8095311955404572116057902609916377656878778047500}{1817704641588239876743}\cdot t^{15}-\frac{16840702657166814601727263303834331581712501531250}{1817704641588239876743}\cdot t^{13}+\frac{24378577682871610020076939467639284190688165865625}{1817704641588239876743}\cdot t^{11}-\frac{46770619343749748736243484345523735856820175559375}{3635409283176479753486}\cdot t^9+\frac{55320492496032159931706082408097641358419554578125}{7270818566352959506972}\cdot t^7-\frac{35973100298760930489856292995027013720579954109375}{14541637132705919013944}\cdot t^5+\frac{10494560168710566235527817684196730065104163859375}{29083274265411838027888}\cdot t^3-\frac{877327576992538328297354672389431885255636890625}{58166548530823676055776}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Hermite (physicists') type can be downloaded here packed into a single file.