Rule: Q[2, 36]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{38}-\frac{6151067763419}{435709684714}\cdot t^{36}+\frac{1892589174553455}{30935387614694}\cdot t^{34}-\frac{115166568226265325}{711513915137962}\cdot t^{32}+\frac{6966428163465981210}{23835716157121727}\cdot t^{30}-\frac{118190006286121113498}{309864310042582451}\cdot t^{28}+\frac{115164162527934153942}{309864310042582451}\cdot t^{26}-\frac{400493995606239979950}{1453978685584425347}\cdot t^{24}+\frac{584531116133358400875}{3729771410847004151}\cdot t^{22}-\frac{255910733286646058775}{3729771410847004151}\cdot t^{20}+\frac{1455660840327490335}{63216464590627189}\cdot t^{18}-\frac{1159495938769765264605}{197677884774891220003}\cdot t^{16}+\frac{220475227224573628650}{197677884774891220003}\cdot t^{14}-\frac{30514044227475791250}{197677884774891220003}\cdot t^{12}+\frac{974543704954697973150}{65036024090939211380987}\cdot t^{10}-\frac{62808263360179655670}{65036024090939211380987}\cdot t^8+\frac{30323473195023056565}{799014010260110311252126}\cdot t^6-\frac{629328867502646025}{799014010260110311252126}\cdot t^4+\frac{58744589538776625}{9061158882311463742497514}\cdot t^2-\frac{3776740822221675}{425874467468638795897383158}$

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.