Rule: Q[20, 31]

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.

• $P_1$:
  $1048576\cdot t^{20}-99614720\cdot t^{18}+3810263040\cdot t^{16}-76205260800\cdot t^{14}+866834841600\cdot t^{12}-5721109954560\cdot t^{10}+21454162329600\cdot t^8-42908324659200\cdot t^6+40226554368000\cdot t^4-13408851456000\cdot t^2+670442572800$
• $P_2$:
  $1048576\cdot t^{51}-\frac{1531697772666304700042372749970636800}{3006477738722676008953699127}\cdot t^{49}+\frac{339800872082618399517137684036281958400}{3006477738722676008953699127}\cdot t^{47}-\frac{45741788657278151297140188368231340441600}{3006477738722676008953699127}\cdot t^{45}+\frac{4188170463607782176064460226315472273408000}{3006477738722676008953699127}\cdot t^{43}-\frac{277124625240510746160501814850280090450001920}{3006477738722676008953699127}\cdot t^{41}+\frac{13744181423553050897220741221291258478853324800}{3006477738722676008953699127}\cdot t^{39}-\frac{523030467105451350539853829533120586085790105600}{3006477738722676008953699127}\cdot t^{37}+\frac{15508618260709669141324551513079922341672637952000}{3006477738722676008953699127}\cdot t^{35}-\frac{361875647837523571179448660286964691794805921536000}{3006477738722676008953699127}\cdot t^{33}+\frac{6684047841643787336354575413271326541303629743001600}{3006477738722676008953699127}\cdot t^{31}-\frac{97988009688246254048612955542631993776232079742208000}{3006477738722676008953699127}\cdot t^{29}+\frac{1140031387806325278151279882790975558115316779991296000}{3006477738722676008953699127}\cdot t^{27}-\frac{10498087340598674585523610668911364956474892505157760000}{3006477738722676008953699127}\cdot t^{25}+\frac{76115334151373752964026572843704538576332359298498400000}{3006477738722676008953699127}\cdot t^{23}-\frac{431043063007145967010394014880338874372555674557948720000}{3006477738722676008953699127}\cdot t^{21}+\frac{1885395472589831883130282198183488562782622928936389650000}{3006477738722676008953699127}\cdot t^{19}-\frac{6274923214287921194125536549654588827958344040516542925000}{3006477738722676008953699127}\cdot t^{17}+\frac{15578393802408745156135446061596887980388022996313864125000}{3006477738722676008953699127}\cdot t^{15}-\frac{28100429651802130821778854340912623586575670247372591062500}{3006477738722676008953699127}\cdot t^{13}+\frac{35546357840873536391205342822398160918061147103365452900000}{3006477738722676008953699127}\cdot t^{11}-\frac{30029857955290809610632835871792796225881145361254580875000}{3006477738722676008953699127}\cdot t^9+\frac{31593490247275261949368870191500104826337379348029320296875}{6012955477445352017907398254}\cdot t^7-\frac{18577642747992838603527114009649007565659569206787414921875}{12025910954890704035814796508}\cdot t^5+\frac{10048369615026694281722716635370944013410801035429741953125}{48103643819562816143259186032}\cdot t^3-\frac{769679417750370574915694903165493979565123437643879765625}{96207287639125632286518372064}\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.