$\vert x\vert^{α+iβ}$类函数多项式逼近误差的渐近性态
Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like $\vert x\vert^{α+iβ}$
摘要：
对$p\in (0,\iy]$给出了一元函数用代数多项式和指数型整函数最佳逼近的$L_p$ -误差之间的新的渐近关系。一般渐近关系适用于函数$\vert x\vert^{\al+i\be},\,\vert x\vert^{\al}\cos(\be\log\vert x\vert)$和$\vert x\vert^{\al}\sin(\be\log\vert x\vert)$。
英文摘要：
New asymptotic relations between the $L_p$-errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $p\in (0,\iy]$. General asymptotic relations are applied to functions $\vert x\vert^{\al+i\be},\,\vert x\vert^{\al}\cos(\be\log\vert x\vert)$, and $\vert x\vert^{\al}\sin(\be\log\vert x\vert)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
