Rule: Q[4, 47]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{51}-\frac{3014525145094298207101964693489854303256}{317748388298858572428944674243562367}\cdot t^{49}+\frac{11783793547728040261636497203629411895721224}{4554393565616972871481540330824393927}\cdot t^{47}-\frac{1963721031222598294440174360825801831879620420}{4554393565616972871481540330824393927}\cdot t^{45}+\frac{6790190608767327850241624561592601349173503520}{138011926230817359741864858509830119}\cdot t^{43}-\frac{4368095018512056958028749384082758395645002960}{1069859893262150075518332236510311}\cdot t^{41}+\frac{546619172824827397902853550243110762188469529035}{2139719786524300151036664473020622}\cdot t^{39}-\frac{52773327954335769299301087908427187600802843542355}{4279439573048600302073328946041244}\cdot t^{37}+\frac{7979213950661897191165809599013906222401489040541575}{17117758292194401208293315784164976}\cdot t^{35}-\frac{476769836949434110547906499296541061656270694625979675}{34235516584388802416586631568329952}\cdot t^{33}+\frac{5658415198801776874644156613931181482550273562911590925}{17117758292194401208293315784164976}\cdot t^{31}-\frac{213830423070971844518420188688304005891578480652749574925}{34235516584388802416586631568329952}\cdot t^{29}+\frac{110797697935337355277698673490419859386170714804949311675}{1180535054634096635054711433390688}\cdot t^{27}-\frac{2638473161952043704514160637317870730341614325301546288375}{2361070109268193270109422866781376}\cdot t^{25}+\frac{98941504991211938023457457045873928865887549156480732479375}{9444280437072773080437691467125504}\cdot t^{23}-\frac{1447177137340147784488980797632061301007186787114311106814375}{18888560874145546160875382934251008}\cdot t^{21}+\frac{65222347617998821284012137170898757092865908281506615135635625}{151108486993164369287003063474008064}\cdot t^{19}-\frac{556749307831863080848805347709430861476545790676800025452713125}{302216973986328738574006126948016128}\cdot t^{17}+\frac{1761596249302844119964593661167053750323476390538363487762965625}{302216973986328738574006126948016128}\cdot t^{15}-\frac{8032016274015480447472477200278170894491607692494940144620615625}{604433947972657477148012253896032256}\cdot t^{13}+\frac{6351150061328809054864871602428965793122499768977043273785615625}{302216973986328738574006126948016128}\cdot t^{11}-\frac{13230279648957581797547498833892946551325189634450519190607178125}{604433947972657477148012253896032256}\cdot t^9+\frac{67413422480775365669142920103706968649990736914040021014723996875}{4835471583781259817184098031168258048}\cdot t^7-\frac{46859713574576368507136286430629360705128931164866683315417421875}{9670943167562519634368196062336516096}\cdot t^5+\frac{29160749845685108583966455882163671562427420289832882376140140625}{38683772670250078537472784249346064384}\cdot t^3-\frac{2595094446405392360052261328293793297238694020944356318651328125}{77367545340500157074945568498692128768}\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.