Best approximation of functions like \(| x|^\lambda\exp (-A| x|^{-a})\)
The author determines the exact orders of best approximation by polynomials and by entire functions of exponential type for the functions: \(\varphi_{\lambda, \alpha,0} (x)= x^\lambda \exp (-Ax^{-\alpha)}\), for \(x>0\), and \(=0\) for \(x\leq 0\); \(\varphi_{\lambda, \alpha,i} (x)= (\text{sgn} x)^{i+1} | x|^\lambda \exp(-A| x|^{-\alpha})\), \(i=1,2\); \(\varphi_{\lambda, \alpha,3} (x)=(a^2-x^2)^\lambda \cdot \exp (-A((a+x)^{-\alpha}+ (a-x)^{-\alpha}))\), for \(| x|<a\), and \(=0\) for \(| x| \geq a\).
scientific article; zbMATH DE number 1197038
scientific article