Rule: Q[3, 10, 22]

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.

• $P_1$:
  $8\cdot t^3-12\cdot t$
• $P_2$:
  $8\cdot t^{13}-\frac{629}{2}\cdot t^{11}+\frac{17435}{4}\cdot t^9-\frac{105435}{4}\cdot t^7+\frac{557865}{8}\cdot t^5-\frac{2248785}{32}\cdot t^3+\frac{1133055}{64}\cdot t$
• $P_3$:
  $8\cdot t^{35}-\frac{1957041419687385592031338609712681}{1041169548055998250022863733340}\cdot t^{33}+\frac{9696925531202360372178218788670551037}{49976138306687916001097459200320}\cdot t^{31}-\frac{1628711726900995036250757940878068631175}{139933187258726164803072885760896}\cdot t^{29}+\frac{1645753115556151343311476511346938655560321}{3638262868726880284879895029783296}\cdot t^{27}-\frac{1388943929942253011288467747493161262291763}{115500408531012072535869683485184}\cdot t^{25}+\frac{364058719364688754622059593697669282458715983}{1617005719434169015502175568792576}\cdot t^{23}-\frac{9741581530050132770614861112085974602118495199}{3234011438868338031004351137585152}\cdot t^{21}+\frac{26734943282103985962448371008342813155030180035}{924003268248096580286957467881472}\cdot t^{19}-\frac{367490989508181877492439611443021093684722990895}{1848006536496193160573914935762944}\cdot t^{17}+\frac{3574790272569616860466666857790935831422103074055}{3696013072992386321147829871525888}\cdot t^{15}-\frac{1856580885973061254279193935525200350848071389835}{568617395844982510945819980234752}\cdot t^{13}+\frac{8443231975521404105849581423801946507307883011105}{1137234791689965021891639960469504}\cdot t^{11}-\frac{24729747304468654744069032643480689722775482051325}{2274469583379930043783279920939008}\cdot t^9+\frac{43562151113534219814435895926332963425659001577775}{4548939166759860087566559841878016}\cdot t^7-\frac{41264607072279405372992746846401841045937885148975}{9097878333519720175133119683756032}\cdot t^5+\frac{17063544790674883176058839445684896043546200760725}{18195756667039440350266239367512064}\cdot t^3-\frac{1868015204665759955430194668363779739204907275425}{36391513334078880700532478735024128}\cdot t$

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.