Rule: Q[3, 32]

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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{35}-\frac{2152343575622569}{99710689090854}\cdot t^{33}+\frac{7077098875860244}{83092240909045}\cdot t^{31}-\frac{131825955085436788}{648119479090551}\cdot t^{29}+\frac{38926979365941668078}{118605864673570833}\cdot t^{27}-\frac{337727958880905978}{892683507557173}\cdot t^{25}+\frac{364989314507940003420}{1136386105120281229}\cdot t^{23}-\frac{231872249241161093972}{1136386105120281229}\cdot t^{21}+\frac{309327758415736440765}{3169919135335521323}\cdot t^{19}-\frac{111133495631715804555}{3169919135335521323}\cdot t^{17}+\frac{207938634077562654860}{22189433947348649261}\cdot t^{15}-\frac{272673766849586147940}{148986199360769502181}\cdot t^{13}+\frac{37814811791774667286}{148986199360769502181}\cdot t^{11}-\frac{460012547284910539370}{19219219717539265781349}\cdot t^9+\frac{2640407207891471040660}{1838638686311256426415721}\cdot t^7-\frac{12926867343966558180}{262662669473036632345103}\cdot t^5+\frac{200089254687957220795}{252681488033061240315989086}\cdot t^3-\frac{6710008765992630747}{1768770416231428682211923602}\cdot t$

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.