Rule: Q[4, 29]

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.

• $P_1$:
  $16\cdot t^4-48\cdot t^2+12$
• $P_2$:
  $16\cdot t^{33}-\frac{24829734601382932392}{6594497324768119}\cdot t^{31}+\frac{63870994450621183605384}{164862433119202975}\cdot t^{29}-\frac{3794935047615545395694202}{164862433119202975}\cdot t^{27}+\frac{11143965705436400220238176}{12681725624554075}\cdot t^{25}-\frac{23027323480469799204456729}{1014538049964326}\cdot t^{23}+\frac{412904248811014011199410339}{1014538049964326}\cdot t^{21}-\frac{20767152059304545103623676801}{4058152199857304}\cdot t^{19}+\frac{182844481668627811772072081133}{4058152199857304}\cdot t^{17}-\frac{4456613667780268932301098239043}{16232608799429216}\cdot t^{15}+\frac{18373590097838079639705836580915}{16232608799429216}\cdot t^{13}-\frac{197700635846725100154623754431235}{64930435197716864}\cdot t^{11}+\frac{20511033998251917829099633257015}{4058152199857304}\cdot t^9-\frac{1232193814059293061364710130163355}{259721740790867456}\cdot t^7+\frac{564809432599814013540477808920045}{259721740790867456}\cdot t^5-\frac{380249454835700665384917576888675}{1038886963163469824}\cdot t^3+\frac{21319584031338563129540929715475}{2077773926326939648}\cdot t$

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.