Rule: Q[5, 8, 14]

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.

• $P_1$:
  $32\cdot t^5-160\cdot t^3+120\cdot t$
• $P_2$:
  $32\cdot t^{13}-\frac{2720}{3}\cdot t^{11}+\frac{26008}{3}\cdot t^9-34608\cdot t^7+59262\cdot t^5-41790\cdot t^3+\frac{19215}{2}\cdot t$
• $P_3$:
  $32\cdot t^{27}-\frac{1443864357088440558448}{375814988811315009}\cdot t^{25}+\frac{219045878311842932409760}{1127444966433945027}\cdot t^{23}-\frac{6139264351369773641772608}{1127444966433945027}\cdot t^{21}+\frac{35212422774388814418292178}{375814988811315009}\cdot t^{19}-\frac{389462550966169308065806627}{375814988811315009}\cdot t^{17}+\frac{2818925261987632959083990396}{375814988811315009}\cdot t^{15}-\frac{4447279158428682739137820300}{125271662937105003}\cdot t^{13}+\frac{9842432068968480385513453435}{91106663954258184}\cdot t^{11}-\frac{37213821308029265617366690405}{182213327908516368}\cdot t^9+\frac{6878199546909544787730687345}{30368887984752728}\cdot t^7-\frac{509393332044354126331111695}{3796110998094091}\cdot t^5+\frac{17551931606509521536927327625}{485902207756043648}\cdot t^3-\frac{2989529438334911095439436075}{971804415512087296}\cdot t$

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.