Rule: Q[2, 10, 13]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{12}-\frac{3091}{728}\cdot t^{10}+\frac{61875}{13832}\cdot t^8-\frac{36135}{16796}\cdot t^6+\frac{7755}{16796}\cdot t^4-\frac{15543}{436696}\cdot t^2+\frac{189}{436696}$
• $P_3$:
  $\frac{3}{2}\cdot t^{25}-\frac{124569197747464699015721812363475}{13477109176722168565021387624216}\cdot t^{23}+\frac{6409271072453514349652499315088925}{256065074357721202735406364860104}\cdot t^{21}-\frac{2118469852977395711221834934594957275}{54102892139295665549380859089727688}\cdot t^{19}+\frac{10361501718568423504949753461823103725}{264819419418657731373285257649719736}\cdot t^{17}-\frac{879876681494639589555861998601844325}{33751494631789710861301062249474084}\cdot t^{15}+\frac{34462923696356009994506341669915992575}{2936380032965704844933192415704245308}\cdot t^{13}-\frac{7199776115964096862113850565275171825}{2032878484360872584953748595487554444}\cdot t^{11}+\frac{1100307167203723739794422921003189845}{1581127710058456454964026685379209012}\cdot t^9-\frac{38032725490974083273027904816169975}{451750774302416129989721910108345432}\cdot t^7+\frac{146141532071725536513862870289195851}{25749794135237719409414148876175689624}\cdot t^5-\frac{25732288924351474799873167699464775}{145915500099680409986680176964995574536}\cdot t^3+\frac{78294763639199830247933848118525}{48638500033226803328893392321665191512}\cdot t$

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.