Rule: Q[45]

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.

• $P_1$:
  $\frac{6489213830472088210604445}{2199023255552}\cdot t^{45}-\frac{36091694899816670384822475}{1099511627776}\cdot t^{43}+\frac{374606902236028199511433275}{2199023255552}\cdot t^{41}-\frac{301154568464257964313113025}{549755813888}\cdot t^{39}+\frac{2688620906409821103084539175}{2199023255552}\cdot t^{37}-\frac{2210643856381408462536176655}{1099511627776}\cdot t^{35}+\frac{5549928668974422089489557425}{2199023255552}\cdot t^{33}-\frac{339791551161699311601401475}{137438953472}\cdot t^{31}+\frac{2106707617202535731928689145}{1099511627776}\cdot t^{29}-\frac{650930968481148787795317955}{549755813888}\cdot t^{27}+\frac{643596535033473871876497471}{1099511627776}\cdot t^{25}-\frac{63596495556667378643922675}{274877906944}\cdot t^{23}+\frac{80049320277795257696081775}{1099511627776}\cdot t^{21}-\frac{9946956957595860423773475}{549755813888}\cdot t^{19}+\frac{3856983310088190776565225}{1099511627776}\cdot t^{17}-\frac{71659799203824309509955}{137438953472}\cdot t^{15}+\frac{127530151125450042348225}{2199023255552}\cdot t^{13}-\frac{5132792460157432044975}{1099511627776}\cdot t^{11}+\frac{570310273350825782775}{2199023255552}\cdot t^9-\frac{5097112671457231425}{549755813888}\cdot t^7+\frac{419762220002360235}{2199023255552}\cdot t^5-\frac{2039660932956075}{1099511627776}\cdot t^3+\frac{11835556670925}{2199023255552}\cdot t$

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.