Rule: Q[3, 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.

• $P_1$:
  $\frac{5}{2}\cdot t^3-\frac{3}{2}\cdot t$
• $P_2$:
  $\frac{5}{2}\cdot t^{43}-\frac{2807153741979615133}{103405640900972022}\cdot t^{41}+\frac{574368720495273654755}{4187928456489366891}\cdot t^{39}-\frac{2484174003500480231395}{5804321895836140077}\cdot t^{37}+\frac{39316467745554283347505}{42565027236131693898}\cdot t^{35}-\frac{186787319153460529602553}{127695081708395081694}\cdot t^{33}+\frac{1242855012253884469806548}{706192497326730376035}\cdot t^{31}-\frac{16480413486296711861490724}{10027933462039571339697}\cdot t^{29}+\frac{834766976846934650174243497}{691927408880730422439093}\cdot t^{27}-\frac{1203443177826227250434647307}{1717005051666997714941453}\cdot t^{25}+\frac{72307735798407625789688870}{223957180652217093253233}\cdot t^{23}-\frac{237121415456875491367146074}{2015614625869953839279097}\cdot t^{21}+\frac{1380518244194067904981000855}{40984164059355728065341639}\cdot t^{19}-\frac{6041246861439433868327540605}{806021893167329318618385567}\cdot t^{17}+\frac{3082727435817647125214998540}{2418065679501987955855156701}\cdot t^{15}-\frac{1435791969647763621968129300}{8866240824840622504802241237}\cdot t^{13}+\frac{13971533575161096208650277993}{939821527433105985509037571122}\cdot t^{11}-\frac{241247326059800987943101995}{256314962027210723320646610306}\cdot t^9+\frac{3821787586464518591083735}{99678040788359725735807015119}\cdot t^7-\frac{38441514931167549917365}{42719160337868453886774435051}\cdot t^5+\frac{6852091477776915366532055}{686667783270897527776012269009774}\cdot t^3-\frac{53011847975560514091649}{1602224827632094231477361961022806}\cdot t$

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.