Smarandache双阶乘对偶函数的三次均值及加权均值

On the Cubic Mean Value and Weighted Mean Value of the Smarandache Double Factioral Dual Function

利用初等方法研究了Smarandache双阶乘对偶函数S^(**)(n)的三次均值及其加权均值,给出了∑_(n≤x)(S^(**)(n))~3,∑_(n≤x)n^k(S^(**)(n))~3及∑(n≤x(S^(**)(n)~3/n^k)的渐近公式,得到了S^(**)(n)新的分布性质,补充了有关文献的结论.

The quadratic mean value and weighted mean value are studied for the Smaxan- dache double factorial dual function S＊＊ （n） by using elementary methods, the asymptotic formulas are given of ∑n≤x（S^＊＊（n））^3,∑n≤xn^k（S^＊＊（n））^3 and ∑n≤x（S^＊＊（n））^3/nk some new properties axe obtained, and the related conclusions are supplemented for some references.