| 关于Smarandache双阶乘函数sdf（n）的两个问题 |
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| 引用本文： | 樊旭辉,朱熙,闫欣荣. 关于Smarandache双阶乘函数sdf（n）的两个问题[J]. 昆明理工大学学报(自然科学版), 2011, 36(2): 71-74. DOI: 10.3969/j.issn.1007-855x.2011.02.015 |
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| 作者姓名： | 樊旭辉 朱熙 闫欣荣 |
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| 作者单位： | 武警工程学院基础部,陕西西安,710086 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 对于任意的正整数n,Smarandache双阶乘函数sdf（n）定义为最小的正整数m使得n｜m!!,其中m!!={1.3.5…m,2｜n2.4.6…m｜n.即就是sdf（n）=min{m：n｜m!!,m∈N}.主要目的是通过研究lnsdf（n）的值的分布性质,从而将Felice Russo在文献[1]中提出的两个极限问题彻底解决.
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| 关 键 词： | Smarandache双阶乘函数sdf（n） 极限 渐近公式 |
On Two Questions of Smarandache Double Factorial Function |
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| FAN Xu-hui,ZHU Xi,YAN Xin-rong. On Two Questions of Smarandache Double Factorial Function[J]. Journal of Kunming University of Science and Technology(Natural Science Edition), 2011, 36(2): 71-74. DOI: 10.3969/j.issn.1007-855x.2011.02.015 |
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| Authors: | FAN Xu-hui ZHU Xi YAN Xin-rong |
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| Affiliation: | (Foundation Department,Engineering College of Armed Police Force,Xi＇an 710086,China) |
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| Abstract: | For any positive integer n,the Smarandache double factorial sdf（n） is defined as the smallest integer m such that n｜m!!,where m!!={1·3·5…m,2｜n 2·4·6…m｜n.That is sdf（n）=min{m：n｜m!!,m∈N}.The main purpose of this paper is to study the arithmetical properties of lnsdf（n） by the elementary methods,and to solve two problems which were proposed by Felice Russo in reference[1]. |
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| Keywords: | Smarandache double factorial function limit asymptotic formula |
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