Rule: Q[1, 16, 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.

• $P_1$:
  $2\cdot t$
• $P_2$:
  $2\cdot t^{17}-136\cdot t^{15}+3570\cdot t^{13}-46410\cdot t^{11}+\frac{1276275}{4}\cdot t^9-\frac{2297295}{2}\cdot t^7+\frac{16081065}{8}\cdot t^5-\frac{11486475}{8}\cdot t^3+\frac{34459425}{128}\cdot t$
• $P_3$:
  $2\cdot t^{43}-\frac{1352578353572165}{2052842729187}\cdot t^{41}+\frac{200578225677249925}{2052842729187}\cdot t^{39}-\frac{59208580344489276909}{6842809097290}\cdot t^{37}+\frac{126115954542826250196077}{246341127502440}\cdot t^{35}-\frac{2114285554195652798282959}{98536451000976}\cdot t^{33}+\frac{5412083496878520046956371}{8211370916748}\cdot t^{31}-\frac{248758084223542070542490125}{16422741833496}\cdot t^{29}+\frac{34633439322633374785663280179}{131381934667968}\cdot t^{27}-\frac{306112727493524432843186607783}{87587956445312}\cdot t^{25}+\frac{3095335162308968663297568079725}{87587956445312}\cdot t^{23}-\frac{47593784883534988032977647079475}{175175912890624}\cdot t^{21}+\frac{1104616095081852389397260209435125}{700703651562496}\cdot t^{19}-\frac{9559670264986737661534792460311875}{1401407303124992}\cdot t^{17}+\frac{15159040785154537788776900143127625}{700703651562496}\cdot t^{15}-\frac{68780458262194109303588815208484375}{1401407303124992}\cdot t^{13}+\frac{1726503075433078945316498283682708125}{22422516849999872}\cdot t^{11}-\frac{3571035033979765233583255924481986875}{44845033699999744}\cdot t^9+\frac{2268195334172479488547550170054038375}{44845033699999744}\cdot t^7-\frac{1581234628208739836569509974826749625}{89690067399999488}\cdot t^5+\frac{986781076304202437440732742510443125}{358760269599997952}\cdot t^3-\frac{85800767760702964201608540801511875}{717520539199995904}\cdot t$

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.