Rule: Q[5, 8, 18]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{13}-\frac{2720}{3}\cdot t^{11}+\frac{26008}{3}\cdot t^9-34608\cdot t^7+59262\cdot t^5-41790\cdot t^3+\frac{19215}{2}\cdot t$
• $P_3$:
  $32\cdot t^{31}-\frac{232971191230900103700271400912}{40215459959405427123553269}\cdot t^{29}+\frac{1665539353158282322435060459976}{3655950905400493374868479}\cdot t^{27}-\frac{3027813996515684800977171463714524}{147456686517819899453028653}\cdot t^{25}+\frac{434638557155553033849001758983219562}{737283432589099497265143265}\cdot t^{23}-\frac{1671619897514945905401784062267609201}{147456686517819899453028653}\cdot t^{21}+\frac{16964518509749657889881901613814615919}{113428220398322999579252810}\cdot t^{19}-\frac{4024742055578418935400646610482615069767}{2949133730356397989060573060}\cdot t^{17}+\frac{50609363231860838759829946716039534848451}{5898267460712795978121146120}\cdot t^{15}-\frac{6648683945405770262471749247986651105227}{181485152637316799326804496}\cdot t^{13}+\frac{3413745531139248608387179413785123018943}{32997300479512145332146272}\cdot t^{11}-\frac{12232006451373305981873636314656387158043}{65994600959024290664292544}\cdot t^9+\frac{26081017691726688029653205683168621040853}{131989201918048581328585088}\cdot t^7-\frac{29913211028780989772553228386825592222789}{263978403836097162657170176}\cdot t^5+\frac{15504330826220252140491480150362995600035}{527956807672194325314340352}\cdot t^3-\frac{2442872768781915414820215587646931237335}{1055913615344388650628680704}\cdot t$

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.