Rule: Q[3, 46]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{49}-\frac{364937148433476606323}{12071415837704435652}\cdot t^{47}+\frac{10135676284296339348929}{59086403837184869244}\cdot t^{45}-\frac{2886438864438813971455}{4755406239095686772}\cdot t^{43}+\frac{19697922755442586631282425}{13120165813664999803948}\cdot t^{41}-\frac{3148115255363503915440102985}{1141454425788854982943476}\cdot t^{39}+\frac{102192372627814120778329609}{26187213547112732402212}\cdot t^{37}-\frac{9461725953025517421994964703}{2173538724410356789383596}\cdot t^{35}+\frac{13417508994215216556158747135}{3452090915239978430197476}\cdot t^{33}-\frac{1465168266083784646310667125}{522442877976931601504982}\cdot t^{31}+\frac{7231900735040699345328149155}{4398631972644488644929042}\cdot t^{29}-\frac{1785452353799887636859202613}{2275154468609218264618470}\cdot t^{27}+\frac{20616515535940533997648943173}{67664779196044528388467830}\cdot t^{25}-\frac{92106417795841878412580254805}{960839864583832303116243186}\cdot t^{23}+\frac{6361406211733279114660165025}{262047235795590628122611778}\cdot t^{21}-\frac{28670985377563312265968121965}{5852388266101524028071663042}\cdot t^{19}+\frac{9852239254507283461379762546}{12680174576553302060821936591}\cdot t^{17}-\frac{2552051083901213291565279097}{26852134397406992599387630428}\cdot t^{15}+\frac{81143472728959914618995562115}{9281887790037017108521657584612}\cdot t^{13}-\frac{73826032806386053568552588075}{126376472218196309862179491728948}\cdot t^{11}+\frac{194643080430727727593340269955}{7203458916437189662144231028550036}\cdot t^9-\frac{33951163480317850603446967}{42125490739398769954059830576316}\cdot t^7+\frac{11095341391365032786713337}{800384324048576629127136780950004}\cdot t^5-\frac{2679961281742703058226122185}{23797827106936328913837157907986468932}\cdot t^3+\frac{2166237010074911251547725}{7932609035645442971279052635995489644}\cdot t$

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.