Rule: Q[1, 12, 14]

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.

• $P_1$:
  $t$
• $P_2$:
  $t^{13}-\frac{78}{25}\cdot t^{11}+\frac{429}{115}\cdot t^9-\frac{1716}{805}\cdot t^7+\frac{1287}{2185}\cdot t^5-\frac{2574}{37145}\cdot t^3+\frac{429}{185725}\cdot t$
• $P_3$:
  $t^{27}-\frac{4887}{725}\cdot t^{25}+\frac{12109122}{599633}\cdot t^{23}-\frac{2062690074}{58216543}\cdot t^{21}+\frac{5736590789607}{142056681569}\cdot t^{19}-\frac{4274902113141375}{136381890973691}\cdot t^{17}+\frac{17422711867822224708}{1031343926935576111}\cdot t^{15}-\frac{7757714083455663571260}{1226267929126399995979}\cdot t^{13}+\frac{152903247596126139465}{94328302240492307383}\cdot t^{11}-\frac{11781946181505952413}{42876501018405594265}\cdot t^9+\frac{200572021320761302578}{6903116663963300676665}\cdot t^7-\frac{8535217413360695202}{4930797617116643340475}\cdot t^5+\frac{899612877850981029}{18737030945043244693805}\cdot t^3-\frac{125817983821378791}{318529526065735159794685}\cdot t$

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.