Rule: Q[38]

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.

• $P_1$:
  $\frac{861577581086657669325}{34359738368}\cdot t^{38}-\frac{8075853860052271220473}{34359738368}\cdot t^{36}+\frac{34847862546800896362315}{34359738368}\cdot t^{34}-\frac{91782398538757290419055}{34359738368}\cdot t^{32}+\frac{41235570357992405840445}{8589934592}\cdot t^{30}-\frac{53544695837990138927145}{8589934592}\cdot t^{28}+\frac{51897166735282750037079}{8589934592}\cdot t^{26}-\frac{38246211312850099233675}{8589934592}\cdot t^{24}+\frac{43262107878469784379075}{17179869184}\cdot t^{22}-\frac{18820239020577250831575}{17179869184}\cdot t^{20}+\frac{6273413006859083610525}{17179869184}\cdot t^{18}-\frac{1586499487685024450265}{17179869184}\cdot t^{16}+\frac{149669762989153250025}{8589934592}\cdot t^{14}-\frac{20542908645570053925}{8589934592}\cdot t^{12}+\frac{1976431444034436675}{8589934592}\cdot t^{10}-\frac{126155198555389575}{8589934592}\cdot t^8+\frac{19624141997505045}{34359738368}\cdot t^6-\frac{402684172315425}{34359738368}\cdot t^4+\frac{3273855059475}{34359738368}\cdot t^2-\frac{4418157975}{34359738368}$

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.