Rule: Q[2, 46]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{48}-\frac{7459734234330112617264109679}{3436139140032642325238902}\cdot t^{46}+\frac{3709201209326357296998440210805}{6872278280065284650477804}\cdot t^{44}-\frac{101995711968423931017464171664855}{1249505141830051754632328}\cdot t^{42}+\frac{21021527940258214601889450580947825}{2499010283660103509264656}\cdot t^{40}-\frac{3133802705172855776154079160921555355}{4998020567320207018529312}\cdot t^{38}+\frac{350122946220132890385437172324053459505}{9996041134640414037058624}\cdot t^{36}-\frac{29976180793576156109833926266411821492425}{19992082269280828074117248}\cdot t^{34}+\frac{1994445911967242189959117805034075568011675}{39984164538561656148234496}\cdot t^{32}-\frac{51992156906074355034844513288637054906558625}{39984164538561656148234496}\cdot t^{30}+\frac{2132641817683734583000476780477245196013939275}{79968329077123312296468992}\cdot t^{28}-\frac{68851834378392974991855646730521661305272238275}{159936658154246624592937984}\cdot t^{26}+\frac{1744663397750477103561812891224244742442303513125}{319873316308493249185875968}\cdot t^{24}-\frac{34491287198444297930923058203471821505480119856875}{639746632616986498371751936}\cdot t^{22}+\frac{527043468828994698672730466358015451443747786140625}{1279493265233972996743503872}\cdot t^{20}-\frac{6143088852526340765479585983210780741929598865475625}{2558986530467945993487007744}\cdot t^{18}+\frac{53648434142654284263062604191291560133279627705938125}{5117973060935891986974015488}\cdot t^{16}-\frac{685462321878006140558494128255953356543870111916690625}{20471892243743567947896061952}\cdot t^{14}+\frac{3101760203316932779682005089170300692274206069191346875}{40943784487487135895792123904}\cdot t^{12}-\frac{9511390461642477790438971805740873056845116164406421875}{81887568974974271791584247808}\cdot t^{10}+\frac{18558552330414070173671280718371315450396727935886003125}{163775137949948543583168495616}\cdot t^8-\frac{20955301496176753758473166498434222030522592669143409375}{327550275899897087166336991232}\cdot t^6+\frac{11703999921682782240034971844800015995806510061662828125}{655100551799794174332673982464}\cdot t^4-\frac{2379207202901870895467682968711707984478034221454703125}{1310201103599588348665347964928}\cdot t^2+\frac{71049876455415521288593451978149404549185713436484375}{2620402207199176697330695929856}$

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.