Rule: Q[4, 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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{34}-\frac{4542188879693093336}{686534065894227}\cdot t^{32}+\frac{3139335470420148981144}{2974980952208317}\cdot t^{30}-\frac{271991763923113816217540}{2974980952208317}\cdot t^{28}+\frac{14653092749850591024550590}{2974980952208317}\cdot t^{26}-\frac{40396579460771031195867225}{228844688631409}\cdot t^{24}+\frac{1997346214105168100431781475}{457689377262818}\cdot t^{22}-\frac{69379739317743358814936512425}{915378754525636}\cdot t^{20}+\frac{425860955370971355403250861625}{457689377262818}\cdot t^{18}-\frac{14725783633622623307899636762125}{1830757509051272}\cdot t^{16}+\frac{353893639867157573599983140314125}{7323030036205088}\cdot t^{14}-\frac{2886578219842312604205524838285375}{14646060072410176}\cdot t^{12}+\frac{15402614513447053825219864523071125}{29292120144820352}\cdot t^{10}-\frac{50820450670033868440618845998529375}{58584240289640704}\cdot t^8+\frac{94934265573375534203126258585180625}{117168480579281408}\cdot t^6-\frac{86513577793018379986418608001011875}{234336961158562816}\cdot t^4+\frac{57284128499247205673336055183414375}{937347844634251264}\cdot t^2-\frac{2846913802557759570759470087461875}{1874695689268502528}$

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.