函数Sdfp（x）及Sdfp^＊（x）的渐近公式

Two Asymptotic Formulas of Functions of Sdfp （ x ） and Sdfp^＊ （ x ）

对于任意实数x,Sdfp(x)=min{m∈N:px≤m!!},x∈(1,∞);Sdfp*(x)=max{m∈N:m!!≤px},x∈(1,∞).研究了这2个函数的均值性质,并得出2个有趣的渐进公式.

To any real number x, the Smarandarehe function is defined as Sdfp （x） = min {m ∈ N：p^x≤m!!},x ∈ （1,∞）,and the antithesis as Sdfp^＊ （x） = max { m ∈ N ： m ! ! ≤p^x } , x ∈（ 1, ∞）. The asymptotic properties of these two functions are studied;thus, the asymptotic formula about their is obtained.