Rule: Q[2, 10, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{12}-\frac{8477}{76}\cdot t^{10}+\frac{155745}{152}\cdot t^8-\frac{563535}{152}\cdot t^6+\frac{1500975}{304}\cdot t^4-\frac{2132865}{1216}\cdot t^2+\frac{110565}{2432}$
• $P_3$:
  $4\cdot t^{30}-\frac{464618060298268536335966586445135906597}{755353863037880978343815641638803348}\cdot t^{28}+\frac{2689013561339001659670010100492528117988069}{66471139947333526094255776464214694624}\cdot t^{26}-\frac{18126119742904992861155606131661140908665775}{12085661808606095653501050266220853568}\cdot t^{24}+\frac{4626139847561917955504115562470385626001490925}{132942279894667052188511552928429389248}\cdot t^{22}-\frac{141096801233457726833832326626737963682902554055}{265884559789334104377023105856858778496}\cdot t^{20}+\frac{5785532123181821522983553381005568090890277273895}{1063538239157336417508092423427435113984}\cdot t^{18}-\frac{80209415453304433252532377185263112648459781372335}{2127076478314672835016184846854870227968}\cdot t^{16}+\frac{186703221951558124954181778344890941595922857010775}{1063538239157336417508092423427435113984}\cdot t^{14}-\frac{17894575131714664227019713220208610113795574565575}{33235569973666763047127888232107347312}\cdot t^{12}+\frac{1627485608481292279186219674333527670320398759751625}{1546964711501580243648134434076269256704}\cdot t^{10}-\frac{3842818708316602397948655734485184850115028601096825}{3093929423003160487296268868152538513408}\cdot t^8+\frac{2522153966038588395444331971006466288506839097044175}{3093929423003160487296268868152538513408}\cdot t^6-\frac{1604946066155351300643462628219311554610840701516625}{6187858846006320974592537736305077026816}\cdot t^4+\frac{770275830893755016484418219025941920934367496205875}{24751435384025283898370150945220308107264}\cdot t^2-\frac{34004406526346698253109822054542197634570572324875}{49502870768050567796740301890440616214528}$

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.