Rule: Q[2, 43]

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.

• $P_1$:
  $\frac{3}{2}\cdot t^2-\frac{1}{2}$
• $P_2$:
  $\frac{3}{2}\cdot t^{45}-\frac{34977553470695}{2108885727906}\cdot t^{43}+\frac{511077068037998}{5975176229067}\cdot t^{41}-\frac{3304946375613575}{12096088463721}\cdot t^{39}+\frac{1186604906275804015}{1959566331122802}\cdot t^{37}-\frac{17001162269724321689}{17200637795411262}\cdot t^{35}+\frac{622748936612376665}{505901111629743}\cdot t^{33}-\frac{312906041052397364}{261672988774005}\cdot t^{31}+\frac{33921509174842803085}{36930781148971239}\cdot t^{29}-\frac{50835869756657148163}{90416740054377861}\cdot t^{27}+\frac{36214423121749256384}{131619305142448785}\cdot t^{25}-\frac{4996328131767162438430}{46444065474598761267}\cdot t^{23}+\frac{67564654316043267383}{2019307194547772229}\cdot t^{21}-\frac{149234471253221036375}{18173764750929950061}\cdot t^{19}+\frac{193461405708497415170}{123177738867414105969}\cdot t^{17}-\frac{1671805520093499995116}{7267486593177432252171}\cdot t^{15}+\frac{1098051980165430656135}{43604919559064593513026}\cdot t^{13}-\frac{28954220246075914153}{14534973186354864504342}\cdot t^{11}+\frac{41821961398465298050}{385176789438403909365063}\cdot t^9-\frac{74668374060806641115}{19644016261358599377618213}\cdot t^7+\frac{1001359100726241829}{13096010840905732918412142}\cdot t^5-\frac{52882889459941255}{73026907909457392036569402}\cdot t^3+\frac{590702297256227}{289382747014342352025510093}\cdot t$

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.