Rule: Q[3, 20]

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.

• $P_1$:
  $\frac{-1}{6}\cdot t^3+\frac{3}{2}\cdot t^2-3\cdot t+1$
• $P_2$:
  $\frac{-1}{6}\cdot t^{23}+\frac{1860243641478816998822550668022740360689}{23860479164592510634708576413418533526}\cdot t^{22}-\frac{594023836368589312474061968600627395391567}{35790718746888765952062864620127800289}\cdot t^{21}+\frac{432833314532488286883549183120640067434766071}{202814072899036340395022899514057534971}\cdot t^{20}-\frac{37628219860911014643178518922604724862915073100}{202814072899036340395022899514057534971}\cdot t^{19}+\frac{2345905923634574732743732963385686036837644571420}{202814072899036340395022899514057534971}\cdot t^{18}-\frac{108577323524074886332558880193996470923182858206280}{202814072899036340395022899514057534971}\cdot t^{17}+\frac{224162817320293474472127699748258896945145635265080}{11930239582296255317354288206709266763}\cdot t^{16}-\frac{6042766061739426796752193334551662105340302800444160}{11930239582296255317354288206709266763}\cdot t^{15}+\frac{125976952949740021175321459555374961306985704082144000}{11930239582296255317354288206709266763}\cdot t^{14}-\frac{2035728312277737925041761195982922780411919970064934400}{11930239582296255317354288206709266763}\cdot t^{13}+\frac{25457116619328491705857967156099818921722072761019609600}{11930239582296255317354288206709266763}\cdot t^{12}-\frac{245048073633884542462794308326234125390427267353833011200}{11930239582296255317354288206709266763}\cdot t^{11}+\frac{1799324356221732434404190496814022223280791951958691174400}{11930239582296255317354288206709266763}\cdot t^{10}-\frac{9946083076976929097154232127540597521474545772946434560000}{11930239582296255317354288206709266763}\cdot t^9+\frac{40647518869347877862500105221817505075450577534310393344000}{11930239582296255317354288206709266763}\cdot t^8-\frac{119888304176613853568169002995678121033209654794901764096000}{11930239582296255317354288206709266763}\cdot t^7+\frac{247145329995084750275145754443375965452415469822943721472000}{11930239582296255317354288206709266763}\cdot t^6-\frac{341110761957369947934149133121900426991200821067281936384000}{11930239582296255317354288206709266763}\cdot t^5+\frac{297234700816728318886580114024295165522481290622791782400000}{11930239582296255317354288206709266763}\cdot t^4-\frac{150495522512702985666533066567455482437975670374185451520000}{11930239582296255317354288206709266763}\cdot t^3+\frac{39088032028556617712627980423937438590270018107615559680000}{11930239582296255317354288206709266763}\cdot t^2-\frac{4202772455744016423823706944883602061605616556172738560000}{11930239582296255317354288206709266763}\cdot t+\frac{110799097885362448344528759862066277467732508330065920000}{11930239582296255317354288206709266763}$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Laguerre type can be downloaded here packed into a single file.