Rule: Q[2, 3, 4, 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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^5-14\cdot t^3+6\cdot t$
• $P_3$:
  $4\cdot t^9-\frac{142}{3}\cdot t^7+\frac{1399}{9}\cdot t^5-\frac{2965}{18}\cdot t^3+\frac{295}{6}\cdot t$
• $P_4$:
  $4\cdot t^{35}-\frac{37416868408907001350164610342873279623358444517881629}{35698938314212875519871034234589270444069604139811}\cdot t^{33}+\frac{285252499918350706726367558808162738929490224006579802877}{2356129928738049784311488259482891849308593873227526}\cdot t^{31}-\frac{115291645452434364061420262756323262526795872317246292164891}{14136779572428298705868929556897351095851563239365156}\cdot t^{29}+\frac{10101069438667294302645992209165257753034683392387485586725453}{28273559144856597411737859113794702191703126478730312}\cdot t^{27}-\frac{22510821670623937393673385952975452739465997854670551611954275}{2094337714433822030499100675095903866052083442868912}\cdot t^{25}+\frac{41654169958018244605753644410488153266830296616982979939614775}{182116322994245393956443536964861205743659429814688}\cdot t^{23}-\frac{115722757691397332829409919810727571839059406824677936608614825}{33112058726226435264807915811792946498847169057216}\cdot t^{21}+\frac{2553098965416784588549677699611940158616139779251690230917939075}{66224117452452870529615831623585892997694338114432}\cdot t^{19}-\frac{40572002583441250555776569734023110197151641437307831521283882725}{132448234904905741059231663247171785995388676228864}\cdot t^{17}+\frac{460079983914481425880632611416882647323499485613759282945905206875}{264896469809811482118463326494343571990777352457728}\cdot t^{15}-\frac{3659960693568904822830512102115998793048934013148169593435363789375}{529792939619622964236926652988687143981554704915456}\cdot t^{13}+\frac{19882985996759883716699056073130960983491945723343226788441814971625}{1059585879239245928473853305977374287963109409830912}\cdot t^{11}-\frac{70788850608395094578385754739091455110911801838714017309714866569125}{2119171758478491856947706611954748575926218819661824}\cdot t^9+\frac{154844383884378914024499689394540151792991296055544669295022843982375}{4238343516956983713895413223909497151852437639323648}\cdot t^7-\frac{186938820123665265741407368919046665974526001454811946403784182591875}{8476687033913967427790826447818994303704875278647296}\cdot t^5+\frac{102151000078898067830186167829334890717473523162678199600590778511875}{16953374067827934855581652895637988607409750557294592}\cdot t^3-\frac{7956343795587733477005769760097282790008451887153514103373255459375}{16953374067827934855581652895637988607409750557294592}\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.