Rule: Q[2, 47]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{49}-\frac{75850358509163}{4257797072250}\cdot t^{47}+\frac{39262000115140103}{395975127719250}\cdot t^{45}-\frac{3024144293163763}{8799447282650}\cdot t^{43}+\frac{8464751901494072569}{10180960506026050}\cdot t^{41}-\frac{264184199906925966899}{177148712804853270}\cdot t^{39}+\frac{208937114537371961279}{101603512742324750}\cdot t^{37}-\frac{18811715087919362970669}{8433091557612954250}\cdot t^{35}+\frac{2587747769770444903699}{1339373365032645675}\cdot t^{33}-\frac{47561466041029587761653}{35270165279193002775}\cdot t^{31}+\frac{520341274362252307349}{682648360242445215}\cdot t^{29}-\frac{3084895604533903003823}{8827349485893688125}\cdot t^{27}+\frac{3096739266871565601559}{23866537498897749375}\cdot t^{25}-\frac{2632161503536679645209}{67780966496869608225}\cdot t^{23}+\frac{1890267070244196258923}{203342899490608824675}\cdot t^{21}-\frac{1598246761862267943503}{908264951058052750215}\cdot t^{19}+\frac{3924900130543620412723}{15137749184300879170250}\cdot t^{17}-\frac{51554128574618097421147}{1771116654563202862919250}\cdot t^{15}+\frac{17420454803784268942937}{7202541061890358309204950}\cdot t^{13}-\frac{14013551205995105263037}{98065366765737955440713550}\cdot t^{11}+\frac{6337932507780707234863}{1117945181129412692024134470}\cdot t^9-\frac{7051893907123847243}{50908250506803856649550750}\cdot t^7+\frac{297429024524587265723}{164586373888496868547997574750}\cdot t^5-\frac{16021347763067950093}{1678781013662668059189575262450}\cdot t^3+\frac{2627254289632342}{279796835610444676531595877075}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

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