等差项乘积的渐进估计  

The Asymptotic Formulas on the Product of Arithmetic Terms

作　　者：王欢欢[1] 沈有建[1] 彭德军[1] 

机构地区：[1]海南师范大学数学与统计学院,海南海口571158

出　　处：《数学的实践与认识》2016年第6期267-275,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11461018;41361108)

摘　　要：研究了等差项乘积∏ni=1a_i的渐进估计.首先给出了一系列关于等差项乘积的不等式,继而应用Euler-Maclaurin求和公式及Γ函数的Stirling公式:Γ(x+1)^(2πx)^(1/2)(x/e)~x(x→+∞),推导出了∏ni=1a_i的较精确的渐进式,最后,得到了精确化的Wallis公式.The asymptotic formulas on the product of arithmetic terms ^n∏i=1 ai are studied in this paper. At first, a series of new inequalities for the product of arithmetic terms were given.Then an accurate asymptotic formula for ^n∏i=1 aiwas deduced by applying Euler-Maclaurin v - formula and Stirling＇s formula for the gamma function Г（x＋1）-√2πx（x/e）^x（x→＋∞） Moreover, a precise Wallis＇s formula was obtained

关 键 词：等差数列 乘积估计 Euler-Maclaurin公式 STIRLING公式 WALLIS公式 

分 类 号：O212[理学—概率论与数理统计]