Rule: Q[7, 38]

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.

• $P_1$:
  $128\cdot t^7-1344\cdot t^5+3360\cdot t^3-1680\cdot t$
• $P_2$:
  $128\cdot t^{45}-\frac{385601046407310354808839197894650464}{6887765977784474250102784222823}\cdot t^{43}+\frac{841834986506963951213317116640762417872}{75765425755629216751130626451053}\cdot t^{41}-\frac{100602978317247610255067719844713391852511}{75765425755629216751130626451053}\cdot t^{39}+\frac{16201438066088214512676370698573330775786251}{151530851511258433502261252902106}\cdot t^{37}-\frac{1864208036555688966057985938621082150305913623}{303061703022516867004522505804212}\cdot t^{35}+\frac{848148094822858393564514356567854787530492165}{3241301636604458470636604340152}\cdot t^{33}-\frac{13619292266413616787086618871009403463265947325}{1620650818302229235318302170076}\cdot t^{31}+\frac{668627934665672797011567255164666439258527077665}{3241301636604458470636604340152}\cdot t^{29}-\frac{25250322598309037250702336464621065826452688883165}{6482603273208916941273208680304}\cdot t^{27}+\frac{31945563889371882274195075186772732227964276295315}{563704632452949299241148580896}\cdot t^{25}-\frac{1429191840630651293309601276104625148677794156143125}{2254818529811797196964594323584}\cdot t^{23}+\frac{24426112109167064204354977886344775271140754618143625}{4509637059623594393929188647168}\cdot t^{21}-\frac{315758557605655763308824619322816128846691118052489125}{9019274119247188787858377294336}\cdot t^{19}+\frac{3042933308325165608281195921670788174944957670733149125}{18038548238494377575716754588672}\cdot t^{17}-\frac{10715351200373550471378485263472461528328283830466453375}{18038548238494377575716754588672}\cdot t^{15}+\frac{53690507537399505333785818119428756094864811107995814375}{36077096476988755151433509177344}\cdot t^{13}-\frac{184517600443474308328424678891107178154394024669322173125}{72154192953977510302867018354688}\cdot t^{11}+\frac{413146006175578511908047973524178825087237555818173713125}{144308385907955020605734036709376}\cdot t^9-\frac{2234190975845848353343046241750660646038172949229833761875}{1154467087263640164845872293675008}\cdot t^7+\frac{1613666619519183066043286176380616639795254761605815579375}{2308934174527280329691744587350016}\cdot t^5-\frac{496981864782321270134895413711895298223090080722694246875}{4617868349054560659383489174700032}\cdot t^3+\frac{38212832306298129804760493560748714492146332772084396875}{9235736698109121318766978349400064}\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.