Gold 8

Gaussian quadrature

Gold ID

8

Link

https://sigir21.wmflabs.org/wiki/Gaussian_quadrature#math.58.61

Formula

$w_{i}={\frac {1}{p'_{n}(x_{i})}}\int _{a}^{b}\omega (x){\frac {p_{n}(x)}{x-x_{i}}}dx$

TeX Source

w_{i} = \frac{1}{p'_{n}(x_{i})}\int_{a}^{b}\omega(x)\frac{p_{n}(x)}{x-x_{i}}dx

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations
		-

Semantic LaTeX

Translation

w_{i} = \frac{1}{p'_{n}(x_{i})} \int_{a}^{b} \omega(x) \frac{p_{n}(x)}{x-x_{i}} \diff{x}

Expected (Gold Entry)

w_{i} = \frac{1}{p'_{n}(x_{i})} \int_{a}^{b} \omega(x) \frac{p_{n}(x)}{x-x_{i}} \diff{x}

Mathematica

Translation

Expected (Gold Entry)

Subscript[w, i] = Divide[1, Subscript[p\[Prime], n][Subscript[x, i]]]*Integrate[\[Omega][x]*Divide[Subscript[p,n][x], x-Subscript[x,i]], {x, a, b}]

Maple

Translation

Expected (Gold Entry)