Rule: Q[2, 40]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{42}-\frac{11813770368659}{769016982238}\cdot t^{40}+\frac{6649105429506085}{91128512395203}\cdot t^{38}-\frac{641452871560385495}{3007240909041699}\cdot t^{36}+\frac{287067938993507945}{668275757564822}\cdot t^{34}-\frac{14014351434200635609}{22174604682832730}\cdot t^{32}+\frac{1660141509486813386852}{2361595398721685745}\cdot t^{30}-\frac{2185361894897604323212}{3621112944706584809}\cdot t^{28}+\frac{98192465573809035051441}{242614567295341182203}\cdot t^{26}-\frac{51736989785392369906175}{242614567295341182203}\cdot t^{24}+\frac{931859234429666630802}{10548459447623529661}\cdot t^{22}-\frac{18443291931889050531214}{643456026305035309321}\cdot t^{20}+\frac{822583147185867336240335}{113891716655991249749817}\cdot t^{18}-\frac{52934691373761462057555}{37963905551997083249939}\cdot t^{16}+\frac{1189239798611433870300}{5881731846084055151399}\cdot t^{14}-\frac{473969654890010692735868}{22132956936814299534714437}\cdot t^{12}+\frac{6407265988109653476537}{4024173988511690824493534}\cdot t^{10}-\frac{2210063442558155969265}{28169217919581835771454738}\cdot t^8+\frac{221912352814105242055}{94568088730024734375598049}\cdot t^6-\frac{3478282471921517325}{94568088730024734375598049}\cdot t^4+\frac{1838019462999449821}{8132855630782127156301432214}\cdot t^2-\frac{38757791288926567}{170789968246424670282330076494}$

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.