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.

• $P_1$:
  $t^{20}-190\cdot t^{18}+14535\cdot t^{16}-581400\cdot t^{14}+13226850\cdot t^{12}-174594420\cdot t^{10}+1309458150\cdot t^8-5237832600\cdot t^6+9820936125\cdot t^4-6547290750\cdot t^2+654729075$
• $P_2$:
  $t^{51}-\frac{2921481652577027702412362575475}{3006477738722676008953699127}\cdot t^{49}+\frac{1296237457590554807728338943619850}{3006477738722676008953699127}\cdot t^{47}-\frac{348982152231431208016511446901179050}{3006477738722676008953699127}\cdot t^{45}+\frac{63906409661983980958014834996268803000}{3006477738722676008953699127}\cdot t^{43}-\frac{8457172401138633610855157923897707838440}{3006477738722676008953699127}\cdot t^{41}+\frac{838878260714907891676070631182327788015950}{3006477738722676008953699127}\cdot t^{39}-\frac{63846492566583416813947000675429759043675550}{3006477738722676008953699127}\cdot t^{37}+\frac{3786283755056071567706189334248027915447421375}{3006477738722676008953699127}\cdot t^{35}-\frac{176697093670665806239965166155744478415432578875}{3006477738722676008953699127}\cdot t^{33}+\frac{6527390470355261070658765052022779825491825920900}{3006477738722676008953699127}\cdot t^{31}-\frac{191382831422355964938697178794203112844203280746500}{3006477738722676008953699127}\cdot t^{29}+\frac{4453247608618458117778437042152248273887956171841000}{3006477738722676008953699127}\cdot t^{27}-\frac{82016307348427145199403208350870038722460097696545000}{3006477738722676008953699127}\cdot t^{25}+\frac{1189302096115214890062915200682883415255193114039037500}{3006477738722676008953699127}\cdot t^{23}-\frac{13470095718973311469074812965010589824142364829935897500}{3006477738722676008953699127}\cdot t^{21}+\frac{117837217036864492695642637386468035173913933058524353125}{3006477738722676008953699127}\cdot t^{19}-\frac{784365401785990149265692068706823603494793005064567865625}{3006477738722676008953699127}\cdot t^{17}+\frac{3894598450602186289033861515399221995097005749078466031250}{3006477738722676008953699127}\cdot t^{15}-\frac{14050214825901065410889427170456311793287835123686295531250}{3006477738722676008953699127}\cdot t^{13}+\frac{35546357840873536391205342822398160918061147103365452900000}{3006477738722676008953699127}\cdot t^{11}-\frac{60059715910581619221265671743585592451762290722509161750000}{3006477738722676008953699127}\cdot t^9+\frac{63186980494550523898737740383000209652674758696058640593750}{3006477738722676008953699127}\cdot t^7-\frac{37155285495985677207054228019298015131319138413574829843750}{3006477738722676008953699127}\cdot t^5+\frac{10048369615026694281722716635370944013410801035429741953125}{3006477738722676008953699127}\cdot t^3-\frac{769679417750370574915694903165493979565123437643879765625}{3006477738722676008953699127}\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.