Rule: Q[41]

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.

• $P_1$:
  $\frac{53098072606098965203605}{274877906944}\cdot t^{41}-\frac{134384010916670220577025}{68719476736}\cdot t^{39}+\frac{1260488001129780170222475}{137438953472}\cdot t^{37}-\frac{1817067118511761024606425}{68719476736}\cdot t^{35}+\frac{14415399140193304128544305}{274877906944}\cdot t^{33}-\frac{1303310059250353523950581}{17179869184}\cdot t^{31}+\frac{2845254354701476002990705}{34359738368}\cdot t^{29}-\frac{1195831540381779769372905}{17179869184}\cdot t^{27}+\frac{6264729413044846254475965}{137438953472}\cdot t^{25}-\frac{803170437569852083907175}{34359738368}\cdot t^{23}+\frac{645086097476738340407985}{68719476736}\cdot t^{21}-\frac{100944918383096163551175}{34359738368}\cdot t^{19}+\frac{97523056742991208854525}{137438953472}\cdot t^{17}-\frac{2237371072376316532425}{17179869184}\cdot t^{15}+\frac{610192110648086327025}{34359738368}\cdot t^{13}-\frac{29933952597830650005}{17179869184}\cdot t^{11}+\frac{32281713585895799025}{274877906944}\cdot t^9-\frac{348782019535488825}{68719476736}\cdot t^7+\frac{17315419409563275}{137438953472}\cdot t^5-\frac{101259762629025}{68719476736}\cdot t^3+\frac{1412926920405}{274877906944}\cdot t$

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.