Rule: Q[1, 6, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^7-21\cdot t^5+\frac{105}{2}\cdot t^3-\frac{105}{4}\cdot t$
• $P_3$:
  $2\cdot t^{45}-\frac{12050032700228448587776224934207827}{13775531955568948500205568445646}\cdot t^{43}+\frac{52614686656685246950832319790047651117}{303061703022516867004522505804212}\cdot t^{41}-\frac{100602978317247610255067719844713391852511}{4848987248360269872072360092867392}\cdot t^{39}+\frac{16201438066088214512676370698573330775786251}{9697974496720539744144720185734784}\cdot t^{37}-\frac{1864208036555688966057985938621082150305913623}{19395948993441079488289440371469568}\cdot t^{35}+\frac{848148094822858393564514356567854787530492165}{207443304742685342120742677769728}\cdot t^{33}-\frac{13619292266413616787086618871009403463265947325}{103721652371342671060371338884864}\cdot t^{31}+\frac{668627934665672797011567255164666439258527077665}{207443304742685342120742677769728}\cdot t^{29}-\frac{25250322598309037250702336464621065826452688883165}{414886609485370684241485355539456}\cdot t^{27}+\frac{31945563889371882274195075186772732227964276295315}{36077096476988755151433509177344}\cdot t^{25}-\frac{1429191840630651293309601276104625148677794156143125}{144308385907955020605734036709376}\cdot t^{23}+\frac{24426112109167064204354977886344775271140754618143625}{288616771815910041211468073418752}\cdot t^{21}-\frac{315758557605655763308824619322816128846691118052489125}{577233543631820082422936146837504}\cdot t^{19}+\frac{3042933308325165608281195921670788174944957670733149125}{1154467087263640164845872293675008}\cdot t^{17}-\frac{10715351200373550471378485263472461528328283830466453375}{1154467087263640164845872293675008}\cdot t^{15}+\frac{53690507537399505333785818119428756094864811107995814375}{2308934174527280329691744587350016}\cdot t^{13}-\frac{184517600443474308328424678891107178154394024669322173125}{4617868349054560659383489174700032}\cdot t^{11}+\frac{413146006175578511908047973524178825087237555818173713125}{9235736698109121318766978349400064}\cdot t^9-\frac{2234190975845848353343046241750660646038172949229833761875}{73885893584872970550135826795200512}\cdot t^7+\frac{1613666619519183066043286176380616639795254761605815579375}{147771787169745941100271653590401024}\cdot t^5-\frac{496981864782321270134895413711895298223090080722694246875}{295543574339491882200543307180802048}\cdot t^3+\frac{38212832306298129804760493560748714492146332772084396875}{591087148678983764401086614361604096}\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.