  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 $\vert
x\vert^{\al}\sin(\be\log\vert x\vert)$.
