Rule: Q[4, 28]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{32}-\frac{435955075353393408}{116316141446875}\cdot t^{30}+\frac{44656321962975123774}{116316141446875}\cdot t^{28}-\frac{2641675926458285133606}{116316141446875}\cdot t^{26}+\frac{8033415449759354180799}{9305291315750}\cdot t^{24}-\frac{103324574237559359338017}{4652645657875}\cdot t^{22}+\frac{14763901212721415088365031}{37221165263000}\cdot t^{20}-\frac{184956380164691153116671573}{37221165263000}\cdot t^{18}+\frac{6491629672001638013726159283}{148884661052000}\cdot t^{16}-\frac{1971730322689174839268063587}{7444233052600}\cdot t^{14}+\frac{129711774422462865819775245657}{119107728841600}\cdot t^{12}-\frac{348118902497937685088806344513}{119107728841600}\cdot t^{10}+\frac{2306824801252222858384401825201}{476430915366400}\cdot t^8-\frac{1080322934954568922400003096877}{238215457683200}\cdot t^6+\frac{788935122070762840529012013357}{381144732293120}\cdot t^4-\frac{130704094941851621263658091507}{381144732293120}\cdot t^2+\frac{2598735725097010082839189935}{304915785834496}$

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.