Rule: Q[4, 31]

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.

• $P_1$:
  $\frac{35}{8}\cdot t^4-\frac{15}{4}\cdot t^2+\frac{3}{8}$
• $P_2$:
  $\frac{35}{8}\cdot t^{35}-\frac{13196487110802315195}{360426259637619992}\cdot t^{33}+\frac{1146082747469936923713}{8199697406755854818}\cdot t^{31}-\frac{483660613910242558218935}{1500544625436321431694}\cdot t^{29}+\frac{1056558649694078055122840}{2107907926208165820713}\cdot t^{27}-\frac{1711884574264171025346705}{3080788507535011584119}\cdot t^{25}+\frac{2789383063552812193871175}{6161577015070023168238}\cdot t^{23}-\frac{89938799242675009973068635}{326563581798711227916614}\cdot t^{21}+\frac{82211756326633739109662325}{653127163597422455833228}\cdot t^{19}-\frac{72664552947943316684129025}{1684380579803878965043588}\cdot t^{17}+\frac{434808645773440452330601125}{39582943625391155678524318}\cdot t^{15}-\frac{11548757581920821896402275}{5654706232198736525503474}\cdot t^{13}+\frac{76808961453518368722115}{284721742370662377747833}\cdot t^{11}-\frac{121059047987851157166280650}{4984623543683186247231312331}\cdot t^9+\frac{13938136027931415470670225}{9969247087366372494462624662}\cdot t^7-\frac{222417104948381517305472825}{4795207849023225169836522462422}\cdot t^5+\frac{98385401445466022208448875}{134265819772650304755422628947816}\cdot t^3-\frac{11525705591235381694305}{3274776092015861091595673876776}\cdot t$

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.