Rule: Q[5, 28]

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.

• $P_1$:
  $\frac{63}{8}\cdot t^5-\frac{35}{4}\cdot t^3+\frac{15}{8}\cdot t$
• $P_2$:
  $\frac{63}{8}\cdot t^{33}-\frac{22078378374741943639}{342103145757943874}\cdot t^{31}+\frac{145560705712292262203977}{605522567991560656980}\cdot t^{29}-\frac{244566470529210665097262}{454141925993670492735}\cdot t^{27}+\frac{15515258343272141012054769}{19174881319732754137700}\cdot t^{25}-\frac{17498139548608907439789993}{20325374198916719385962}\cdot t^{23}+\frac{7562051451761565667257349}{11328897094478171461028}\cdot t^{21}-\frac{3476587232970425992151877}{9092930562673269198983}\cdot t^{19}+\frac{69345542119332296242160307}{427367736445643652352201}\cdot t^{17}-\frac{89227975695892165259227243}{1759749503011473862626710}\cdot t^{15}+\frac{49668487242498847746947781}{4323955921685335776739916}\cdot t^{13}-\frac{81414666095132228951885468}{44320548197274691711584139}\cdot t^{11}+\frac{105774973473733243044709487}{531846578367296300539009668}\cdot t^9-\frac{845133302863371511554609}{61881520124496739370891062}\cdot t^7+\frac{473864873467772420042673}{886410963945493834231682780}\cdot t^5-\frac{16092651774552123948337}{1639860283299163593328613143}\cdot t^3+\frac{4924214020711415290809}{91832175864753161226402336008}\cdot t$

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.