Rule: Q[2, 3, 6, 16]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^{11}-\frac{6923}{82}\cdot t^9+\frac{97479}{164}\cdot t^7-\frac{566685}{328}\cdot t^5+\frac{1313235}{656}\cdot t^3-\frac{418635}{656}\cdot t$
• $P_4$:
  $4\cdot t^{27}-\frac{18602579712383878626727500047181374637}{37352128661862989611625882764510142}\cdot t^{25}+\frac{192929105341891780923534882307275370184011}{7395721475048871943101924787373008116}\cdot t^{23}-\frac{55950380084413613458467937165969594423074041}{73957214750488719431019247873730081160}\cdot t^{21}+\frac{663864826594708668963424528982895827637682549}{49304809833659146287346165249153387440}\cdot t^{19}-\frac{3801287791192870507782550586682542459572035613}{24652404916829573143673082624576693720}\cdot t^{17}+\frac{2078590764950990084632582196395305710554955567}{1792902175769423501358042372696486816}\cdot t^{15}-\frac{1839187122969481435753377901357387069479940493}{320681689975018837641275871539209024}\cdot t^{13}+\frac{44010590698246551975681326315142359919699322615}{2390536234359231335144056496928649088}\cdot t^{11}-\frac{354948968306563035285879570862895401610640869861}{9562144937436925340576225987714596352}\cdot t^9+\frac{847268809082663823603602552646224294888980760013}{19124289874873850681152451975429192704}\cdot t^7-\frac{1075909353398307023974063851904183537025616991035}{38248579749747701362304903950858385408}\cdot t^5+\frac{585959156894788828875873698514534545937251754645}{76497159499495402724609807901716770816}\cdot t^3-\frac{38989004364594468641511334375185435705024746445}{76497159499495402724609807901716770816}\cdot t$

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.