When the term Gaussian Quadrature appears in most Literatures, does it actually refer to Gauss-Legendre Quadrature.


In other words, do they implicitly admit that they use the Legendre orthogonal polynomials by default?



Does Gaussian Quadrature actually refer to Gauss-Legendre Quadrature？
It is standard to use the term Gaussian Quadrature to refer broadly to any approximation


$$\int\_a^b \omega (w)f(x)dx=\sum\_{i=1}^n w\_if(x\_i)$$


that is optimanl in the sense of Gauss's fundamental theorem of quadrature, *regardless of the associated polynomial*.


In particular, unless the context makes it somehow clear, I would not jump to the conclusion that Gaussian Quadrature means Gauss-Legendre Quadrature, i.e. that $\omega (w)=1$.


For example [Wikipedia](https://en.wikipedia.org/wiki/Gaussian_quadrature) and [Wolfram](http://mathworld.wolfram.com/GaussianQuadrature.html) are consistent with this use.


