Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (3): 960-971.

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New Results On Gauss Product Inequalities (I)

Li Ma1,2(),Pengying Chen1(),Xinfang Han1,2,*()   

  1. 1Department of Mathematics and Statistics, Hainan Normal University, Haikou 571158
    2Key Laboratory of Data Science and Intelligence Education (Hainan Normal University), Ministry of Education, Haikou 571158
  • Received:2024-05-07 Revised:2025-01-13 Online:2025-06-26 Published:2025-06-20
  • Supported by:
    Hainan Provincial Natural Science Foundation(122MS056);Hainan Provincial Natural Science Foundation(124MS056)

Abstract:

Let (X1,X2,X3) be a centered Gaussian random vector with D(Xi)=1, i=1,2,3. By means of the properties of hypergeometric function and factorization, we prove that

E[|X41X32X33|]E|X41|E|X32|E|X33|,

and the equal sign holds if and only if X1,X2,X3 are independent. This complements the results of the three dimensional Gauss product inequality in the existing literature.

Key words: Gauss Product Inequality, normal Distribution, hypergeometric Function, factorization

CLC Number: 

  • O177.2
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