Rule: Q[2, 30]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{32}-\frac{3328368661}{285500252}\cdot t^{30}+\frac{690469043295}{16844514868}\cdot t^{28}-\frac{27594751918545}{320045782492}\cdot t^{26}+\frac{425584315303875}{3520503607412}\cdot t^{24}-\frac{22232015938612935}{186586691192836}\cdot t^{22}+\frac{24467073951193965}{288361250025292}\cdot t^{20}-\frac{4693223668164525}{106238355272476}\cdot t^{18}+\frac{4942312805391975}{293717805753316}\cdot t^{16}-\frac{23124916429875}{4978267894124}\cdot t^{14}+\frac{1643656507154805}{1804266521056084}\cdot t^{12}-\frac{9081791544829185}{73974927363299444}\cdot t^{10}+\frac{798235004493225}{73974927363299444}\cdot t^8-\frac{1557706385810925}{2737072312442079428}\cdot t^6+\frac{299172295141875}{19159506187094555996}\cdot t^4-\frac{35273381967045}{210754568058040115956}\cdot t^2+\frac{61808718915}{210754568058040115956}$

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.