δ函数的导函数的Legendre非线性逼近

Legendre nonlinear approximations to the derivative of delta function

讨论了利用变形Legendre多项式母函数的非线性逼近.当这类非线性逼近应用于D iracδ函数的导函数时,它们被证明是Gauss求积公式应用于这一导函数的含有前述母函数的Stieltjes积分表示式.进一步证得了收敛性,导出了逼近误差.

The nonlinear approximations based on the modified generating functions of the Legendre polynomlals were studied. It was showed that such nonlinear approximations to the derivative of Dirac delta function on in [-1,1 ] were the corresponding Gaussian quadratures applied to its Stieltjes integral representations, whose tegrands contain weights and the modified generating functions of Legendre polynomials. In addition, the convergence was proved and the error term was presented.