Rule: Q[2, 37]

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.

• $P_1$:
  $4\cdot t^2-2$
• $P_2$:
  $4\cdot t^{39}-\frac{822573394833612952982}{555847452794224045}\cdot t^{37}+\frac{136759913960259947567121}{555847452794224045}\cdot t^{35}-\frac{773847693524098917955521}{31762711588241374}\cdot t^{33}+\frac{25499843862021918390012759}{15881355794120687}\cdot t^{31}-\frac{2368032386910617241336879225}{31762711588241374}\cdot t^{29}+\frac{160003198938199600899240696063}{63525423176482748}\cdot t^{27}-\frac{616253938825297249805217034761}{9773142027151192}\cdot t^{25}+\frac{46151451130958274353502210995925}{39092568108604768}\cdot t^{23}-\frac{1295468420339430167535347281038675}{78185136217209536}\cdot t^{21}+\frac{27164933669947032409800447245696625}{156370272434419072}\cdot t^{19}-\frac{421670928880271941139301897438033075}{312740544868838144}\cdot t^{17}+\frac{2385953491596535841539666954502553975}{312740544868838144}\cdot t^{15}-\frac{19242771580885440134265033189992819625}{625481089737676288}\cdot t^{13}+\frac{107051547636593648626811071164447918375}{1250962179475352576}\cdot t^{11}-\frac{391942348944550860520438367658002848125}{2501924358950705152}\cdot t^9+\frac{3522261208994325084683125269417269959875}{20015394871605641216}\cdot t^7-\frac{4344580401602443583431082931068400001125}{40030789743211282432}\cdot t^5+\frac{2410073472732099838506901601260226499375}{80061579486422564864}\cdot t^3-\frac{379972289494132967999452880128808368125}{160123158972845129728}\cdot t$

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.