Rule: Q[1, 14, 26]

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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{15}-105\cdot t^{13}+\frac{4095}{2}\cdot t^{11}-\frac{75075}{4}\cdot t^9+\frac{675675}{8}\cdot t^7-\frac{2837835}{16}\cdot t^5+\frac{4729725}{32}\cdot t^3-\frac{2027025}{64}\cdot t$
• $P_3$:
  $2\cdot t^{41}-\frac{22833095501}{29775546}\cdot t^{39}+\frac{43032537434107}{337456188}\cdot t^{37}-\frac{8304039802133725}{674912376}\cdot t^{35}+\frac{3136019764574738405}{4049474256}\cdot t^{33}-\frac{45637553363092736045}{1349824752}\cdot t^{31}+\frac{318279662003627429105}{299961056}\cdot t^{29}-\frac{132035441989742569212935}{5399299008}\cdot t^{27}+\frac{502649899038914541839925}{1199844224}\cdot t^{25}-\frac{3217837084812588393280125}{599922112}\cdot t^{23}+\frac{61582771925236553429563125}{1199844224}\cdot t^{21}-\frac{46128475296459198538520625}{126299392}\cdot t^{19}+\frac{56858910751174146192703125}{29717504}\cdot t^{17}-\frac{863306759551137794893625625}{118870016}\cdot t^{15}+\frac{4640525842657720742454853125}{237740032}\cdot t^{13}-\frac{17091847151835262339835176875}{475480064}\cdot t^{11}+\frac{10288928503503825314155891875}{237740032}\cdot t^9-\frac{120914547492846549612221926875}{3803840512}\cdot t^7+\frac{97380998467467210486349734375}{7607681024}\cdot t^5-\frac{35895439572223163460743840625}{15215362048}\cdot t^3+\frac{4080072969924076582065984375}{30430724096}\cdot t$

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.