Rule: Q[40]

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.

• $P_1$:
  $\frac{26876802183334044115405}{274877906944}\cdot t^{40}-\frac{66341473743672640538025}{68719476736}\cdot t^{38}+\frac{605689039503920341535475}{137438953472}\cdot t^{36}-\frac{847964655305488478149665}{68719476736}\cdot t^{34}+\frac{6516550296251767619752905}{274877906944}\cdot t^{32}-\frac{569050870940295200598141}{17179869184}\cdot t^{30}+\frac{1195831540381779769372905}{34359738368}\cdot t^{28}-\frac{481902262541911250344305}{17179869184}\cdot t^{26}+\frac{2409511312709556251721525}{137438953472}\cdot t^{24}-\frac{293220953398517427458175}{34359738368}\cdot t^{22}+\frac{222078820442811559812585}{68719476736}\cdot t^{20}-\frac{32507685580997069618175}{34359738368}\cdot t^{18}+\frac{29085823940892114921525}{137438953472}\cdot t^{16}-\frac{610192110648086327025}{17179869184}\cdot t^{14}+\frac{149669762989153250025}{34359738368}\cdot t^{12}-\frac{6456342717179159805}{17179869184}\cdot t^{10}+\frac{5929294332103310025}{274877906944}\cdot t^8-\frac{51946258228689825}{68719476736}\cdot t^6+\frac{1923935489951475}{137438953472}\cdot t^4-\frac{7064634602025}{68719476736}\cdot t^2+\frac{34461632205}{274877906944}$

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.