Rule: Q[20, 35]

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^{55}-\frac{1617450184723481142500351533465}{1439353401094042506073400538}\cdot t^{53}+\frac{9663934114002430438277674755070690}{16552564112581488819844106187}\cdot t^{51}-\frac{22633109901028635914954758723878486925}{121385470158930918012190112038}\cdot t^{49}+\frac{2491591485032028572290906354458582832750}{60692735079465459006095056019}\cdot t^{47}-\frac{402049150562645566158491411333387844418405}{60692735079465459006095056019}\cdot t^{45}+\frac{49345758110173372634578063992419258637220800}{60692735079465459006095056019}\cdot t^{43}-\frac{4719177675869805105024352751949539179055427075}{60692735079465459006095056019}\cdot t^{41}+\frac{15538859908128931782190513483695390027430543875}{2638814568672411261134567653}\cdot t^{39}-\frac{3939363320495794918677510590355611204578777401375}{11035042741720992546562737458}\cdot t^{37}+\frac{1058782433245751897171728823700620246636962463263050}{60692735079465459006095056019}\cdot t^{35}-\frac{7612864963204456785755498292498142457542189610722125}{11035042741720992546562737458}\cdot t^{33}+\frac{121993305180820915336004122616873131343236643583595500}{5517521370860496273281368729}\cdot t^{31}-\frac{137660862402977457190806975134696428701031553336733750}{239892233515673751012233423}\cdot t^{29}+\frac{66358062640606501239826195052424863437618936737973890000}{5517521370860496273281368729}\cdot t^{27}-\frac{1117547717070481876104509564317006400082140250823212783750}{5517521370860496273281368729}\cdot t^{25}+\frac{15016105071263584677822643565149572674790319435072049634375}{5517521370860496273281368729}\cdot t^{23}-\frac{13864072992769955596811346351531959554334642607145639603125}{479784467031347502024466846}\cdot t^{21}+\frac{57435153276329142662409125233846891688805161142571409718750}{239892233515673751012233423}\cdot t^{19}-\frac{730764101697366605018505203633836194519293057643132147984375}{479784467031347502024466846}\cdot t^{17}+\frac{1747806276517156098042662907120883510998470372377928440443750}{239892233515673751012233423}\cdot t^{15}-\frac{6117473506340718840308388013001127194412665668651164946640625}{239892233515673751012233423}\cdot t^{13}+\frac{15107528218921386227929387554977402651608523905650771251250000}{239892233515673751012233423}\cdot t^{11}-\frac{25037541456114778088123192160974200278311805698116148137734375}{239892233515673751012233423}\cdot t^9+\frac{25895722170111905470748617607703816783467729776453937816484375}{239892233515673751012233423}\cdot t^7-\frac{29840586116328757156238987596946094053035661541468939677109375}{479784467031347502024466846}\cdot t^5+\frac{3915027382764580455728528471514214492642607868506061808593750}{239892233515673751012233423}\cdot t^3-\frac{590723060430682154443963092740687252745393152679878698828125}{479784467031347502024466846}\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.