In numerical analysis Chebyshev–Gauss quadrature is an extension of Gaussian quadrature method for approximating the value of integrals of the following kind: ∫ − 1 + 1 f ( x ) 1 − x 2 d x {\displaystyle \int _{-1}^{+1}{\frac {f(x)}{\sqrt {1-x^{2}}}}\,dx} and ∫ − 1 + 1 1 − x 2 g ( x ) d x . {\displaystyle \int _{-1}^{+1}{\sqrt {1-x^{2}}}g(x)\,dx.} In the first case ∫ − 1 + 1 f ( x ) 1 − x 2 d x ≈ ∑ i = 1 n w i f ( x i ) {\displaystyle \int _{-1}^{+1}{\frac {f(x)}{\sqrt {1-x^{2}}}}\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i})} where x i = cos ( 2 i − 1 2 n π ) {\displaystyle x_{i}=\cos \left({\frac {2i-1}{2n}}\pi \right)} and the weight w i = π n . {\displaystyle w_{i}={\frac {\pi }{n}}.} [1] In the second case ∫ − 1 + 1 1 − x 2 g ( x ) d x ≈ ∑ i = 1 n w i g ( x i ) {\displaystyle \int _{-1}^{+1}{\sqrt {1-x^{2}}}g(x)\,dx\approx \sum _{i=1}^{n}w_{i}g(x_{i})} where x i = cos ( i n + 1 π ) {\displaystyle x_{i}=\cos \left({\frac {i}{n+1}}\pi \right)} and the weight w i = π n + 1 sin 2 ( i n + 1 π ) . {\displaystyle w_{i}={\frac {\pi }{n+1}}\sin ^{2}\left({\frac {i}{n+1}}\pi \right).\,} [2] See also Chebyshev polynomials Chebyshev nodes ReferencesLoading content...External linksLoading content...Loading related searches...Wikiwand - on Seamless Wikipedia browsing. On steroids.