Rule: Q[4, 10, 23]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{14}-\frac{3816}{7}\cdot t^{12}+\frac{44964}{7}\cdot t^{10}-\frac{225630}{7}\cdot t^8+68715\cdot t^6-\frac{108945}{2}\cdot t^4+\frac{46845}{4}\cdot t^2-\frac{2835}{8}$
• $P_3$:
  $16\cdot t^{37}-\frac{49809463975510789629375582642143499672}{9317405211111424789646489158029125}\cdot t^{35}+\frac{6806277167854517122577141493848354345256}{9317405211111424789646489158029125}\cdot t^{33}-\frac{517842726528494987856874555432475345116344}{9317405211111424789646489158029125}\cdot t^{31}+\frac{64550863379083319227901606179277777991378984}{24225253548889704453080871810875725}\cdot t^{29}-\frac{1118701615153991412102037938605976046662760236}{13044367295555994705505084821240775}\cdot t^{27}+\frac{325456237581744218830534610400439092917361127473}{169576774842227931171566102676130075}\cdot t^{25}-\frac{10323482778137903115670102538906087245131330901173}{339153549684455862343132205352260150}\cdot t^{23}+\frac{302584777644225259691442986656671774825325161129}{876932255163428215496140156049800}\cdot t^{21}-\frac{216800628191994729643923485465463319225348767610239}{77520811356447054249858789794802320}\cdot t^{19}+\frac{311998869145660218403018732833136334095243156866381}{19380202839111763562464697448700580}\cdot t^{17}-\frac{84572556775899769962142678088794484310670091424639}{1302870779099950491594265374702560}\cdot t^{15}+\frac{1676012474689949457000917277356963430473635635939}{9344360096003743279876903302170}\cdot t^{13}-\frac{230735635327243880068563654436240263324064004327757}{701545804130742572396912124839840}\cdot t^{11}+\frac{428875416795723356967615694364418304034882438726469}{1122473286609188115835059399743744}\cdot t^9-\frac{84075533332357916572366332000114003807912393518139}{320706653316910890238588399926784}\cdot t^7+\frac{241928371312403394361155293027901613139704049285979}{2565653226535287121908707199414272}\cdot t^5-\frac{71011801504343804759464408169161466973021180635709}{5131306453070574243817414398828544}\cdot t^3+\frac{1990007550000125048719189418943036072754839272841}{5131306453070574243817414398828544}\cdot t$

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.