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《Mathematics in Practice and Theory》 2013-16
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On the Cubic Mean Value and Weighted Mean Value of the Smarandache Double Factioral Dual Function

WANG Yang;School of Mathematics and Statistics,Nanyang Normal University;  
The quadratic mean value and weighted mean value axe studied for the Smarandache double factorial dual function S**(n) by using elementary methods,the asymptotic formulas are given of Σ_(n≤x)(S**(n))~3,Σ_(n≤x)n~k(S**(n))~3,and Σ_(n≤x)((s**(n))~3)/(n~k),some new properties are obtained,and the related conclusions are supplemented for some references.
【Fund】: 国家自然科学基金(11071194);; 河南省自然科学基金(132300410372)
【CateGory Index】: O156.4
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【Citations】
Chinese Journal Full-text Database 7 Hits
1 GOU Su Department of Applied Mathematics and Physics,Xi'an Institute of Posts and Telecommunications,Xi'an 710061,China DU Xiao-ying Department of Mathematics,Northwest University,Xi'an 710127,China;On the Smarandache dual functions[J];Pure and Applied Mathematics;2008-01
2 Yang Yanting(Department of Mathematics, Northwest University, Xi’an 710127, China);On the mean value of a number theoretic function[J];Journal of Natural Science of Heilongjiang University;2008-03
3 WANG Yang(School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China);On some equations involving the Smarandache double factorial dual function[J];Journal of Nanyang Normal University;2010-03
4 WANG Yang (School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China);An identity of the Smarandache double factorial dual function[J];Journal of Nanyang Normal University;2012-12
5 Zhe Feng XU Department of Mathematics, Northwest University, Xi'an 710069, P. R. China;On the Value Distribution of the Smarandache Function[J];Acta Mathematica Sinica;2006-05
6 Jie LI Department of Mathematics,Northwest University,Xi'an 710069,P.R.China;An Equation Involving the Smarandache Primitive Function[J];Acta Mathematica Sinica;2007-02
7 LIU Yan-ni(Department of Mathematics,Northwest University,Xi′an 710069,China);An equation involving the Smarandache function[J];Journal of Northwest University(Natural Science Edition);2007-02
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 DU Fengying(Zhgjiang Jinhua College of Profession and Technology,Jinhua 321017,China);On a conjecture of the Smarandache function S(n)[J];Pure and Applied Mathematics;2007-02
2 SHEN Hong(Xianyang Vocational and Technical College,Xianyang 712000,China);A new arithmetical function and its value distribution[J];Pure and Applied Mathematics;2007-02
3 XUE Shejiao(Department of Mathematics,Weinan Teacher′s College,Weinan 714000,China);A new arithmetical function and its mean value[J];Pure and Applied Mathematics;2007-03
4 WU Qibin(Department of Mathematics,Xianyang Normal College,Xianyang 712000,China);A composite function involving the Smarandache function[J];Pure and Applied Mathematics;2007-04
5 ZHOU Huan-qin (Department of Mathematics,Weinan Teacher's College,Weinan 714000,China);On the Smarandache function and the Riemann zeta-function[J];Pure and Applied Mathematics;2008-01
6 XIONG Wen-jing (Department of Mathematics and Physics,Shaanxi Institute of Education,Xi'an 710061,China);On the parity of the Smarandache function[J];Pure and Applied Mathematics;2008-02
7 ZHANG Ai-ling (Faculty of Higher Technical,Xi'an University of Technology,Xi'an 710082,China);On a problem of the Smarandache function[J];Pure and Applied Mathematics;2008-02
8 GE Jian School of Statistics, Xi'an University of Finance and Economics, Xi'an 710061, China;On the value distribution problems of the Smarandache double-factorial function[J];Pure and Applied Mathematics;2008-03
9 FAN Xu-hui1,2,ZHAO Chun-xiang2(1.Foundation Department,Engineering College of Armed Police Force,Xi’an 710086,China;2.Department of Mathematics,Northwest University,Xi’an 710127,China);On the hybrid mean value of the Smarandache function and the Dirichlet divisor function[J];Pure and Applied Mathematics;2008-04
10 LI Fan-bei(School of Mathematics and Statistics,Inner Mongolia Finance and Economics College Hohhot 010051,China);A new Smarandache function and its mean value[J];Pure and Applied Mathematics;2008-04
【Secondary Citations】
Chinese Journal Full-text Database 9 Hits
1 ZHAO Yuan-e(College of Mathematics and Computer Science,Yanan University,Yanan 716000,China);An new arithmetical function and its mean value[J];Pure and Applied Mathematics;2006-02
2 Zhu Weiyi (College of Mathematics,Physics and Information Engineer Zhejiang Normal University,Jinhua 321004,China);On the asymptotic property of the F. Smarandache function S(m~n)[J];Pure and Applied Mathematics;2007-01
3 GOU Su Department of Applied Mathematics and Physics,Xi'an Institute of Posts and Telecommunications,Xi'an 710061,China DU Xiao-ying Department of Mathematics,Northwest University,Xi'an 710127,China;On the Smarandache dual functions[J];Pure and Applied Mathematics;2008-01
4 ZHOU Huan-qin (Department of Mathematics,Weinan Teacher's College,Weinan 714000,China);On the Smarandache function and the Riemann zeta-function[J];Pure and Applied Mathematics;2008-01
5 LIU Yan-ni, PAN Xiao-wei (Department of Mathematics, Northwest University Xi’an, Shanxi 710069, China);Two equations involving the Smarandache function and its solutions[J];Journal of Natural Science of Heilongjiang University;2006-06
6 Yang Yanting(Department of Mathematics, Northwest University, Xi’an 710127, China);On the mean value of a number theoretic function[J];Journal of Natural Science of Heilongjiang University;2008-03
7 WANG Yang(School of Mathematics and Statistics,Nanyang Normal University,Nanyang 473061,China);On some equations involving the Smarandache double factorial dual function[J];Journal of Nanyang Normal University;2010-03
8 Zhe Feng XU Department of Mathematics, Northwest University, Xi'an 710069, P. R. China;On the Value Distribution of the Smarandache Function[J];Acta Mathematica Sinica;2006-05
9 CHEN Guo-hui~1,LIU Hua-ning~2 (1.Department of Mathematics,Hainan Normal University,Haikou 571158,China;2.Department of Mathematics,Northwest University,Xi′an 710069,China);On a equation in a finite field and the calculating formula for its number of solutions[J];Journal of Northwest University(Natural Science Edition);2004-03
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