Rule: Q[6, 30]

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.

• $P_1$:
  $64\cdot t^6-480\cdot t^4+720\cdot t^2-120$
• $P_2$:
  $64\cdot t^{36}-\frac{42503236931443145123450160}{2488892854245165044521}\cdot t^{34}+\frac{5005121321862455135530216680}{2488892854245165044521}\cdot t^{32}-\frac{344054453380127244478886737890}{2488892854245165044521}\cdot t^{30}+\frac{15391729136310544717591922053875}{2488892854245165044521}\cdot t^{28}-\frac{72786415058495527276892764988235}{382906592960794622234}\cdot t^{26}+\frac{3165176191261639109995471976020125}{765813185921589244468}\cdot t^{24}-\frac{98795812568849147272809378441227625}{1531626371843178488936}\cdot t^{22}+\frac{2224289382915994064949739918865128875}{3063252743686356977872}\cdot t^{20}-\frac{1895942383864188837719148376050290625}{322447657230142839776}\cdot t^{18}+\frac{21879332220218868759292261099503573375}{644895314460285679552}\cdot t^{16}-\frac{177001108207600483457380738004604733125}{1289790628920571359104}\cdot t^{14}+\frac{979752939817725556365996556823894889375}{2579581257841142718208}\cdot t^{12}-\frac{3583217614676060125820730780642238576875}{5159162515682285436416}\cdot t^{10}+\frac{8218734850027817475251502850482658078125}{10318325031364570872832}\cdot t^8-\frac{10862590858832592833964209830320808820625}{20636650062729141745664}\cdot t^6+\frac{7080913132669906868124047827249262184375}{41273300125458283491328}\cdot t^4-\frac{1622514288489944788399913056132416590625}{82546600250916566982656}\cdot t^2+\frac{44214631502094292917589239503860059375}{165093200501833133965312}$

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.