On the Gaussian integration of Chebyshev polynomials
Copyright policy )On the Gaussian integration of Chebyshev polynomials
It is shown that as m m tends to infinity, the error in the integration of the Chebyshev polynomial of the first kind, T ( 4 m + 2 ) j ± 2 l ( x ) {T_{(4m + 2)j \pm 2l}}(x) , by an m m -point Gauss integration rule approaches ( − 1 ) j ⋅ 2 / ( 4 l 2 − 1 ) , l = 0 , 1 , ⋯ , m − 1 {( - 1)^j} \cdot 2/(4{l^2} - 1),l = 0,1, \cdots ,m - 1 , and ( − 1 ) j ⋅ π / 2 , l = m {( - 1)^j} \cdot \pi /2,l = m , for all j j .
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Numerical integration
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Numerical integration
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