新常数μ,θ和新公式π=(1/2)e~θ的含义与应用  

The Meaning and Applications of the Constantsμ,θ and the formula π=(1/2)e~θ

作　　者：陈文伟[1] 

机构地区：[1]海军兵种指挥学院信息与决策教研室,广东广州510431

出　　处：《高等数学研究》2015年第3期31-33,37,共4页Studies in College Mathematics

摘　　要：作者在文献[1]和[2]中提出了新常数μ,θ和新公式π=1/2 e~θ.在此说明它的深层含义:新常数μ是隐藏在欧拉常数γ后面的常数;新常数θ是μ和γ的完美组合.新公式给出了π和e之间的实数关系,它不同于欧拉公式e^(πi)=-1的虚数关系.新公式的典型应用是π和e之间的转换,以及μ和γ之间的转换.本文利用μ的计算公式,进行计算机求解,通过新公式,能很快求出欧拉常数γ.本文对概率统计中很多常用公式,用e^(θ/2)号代替(2π)^(1/2),极大简化了这些公式.In [1] and [2], two new constants μ and θ and a new formula π=1/2eθ were introduced. This paper explains their deep meanings： the constant μ is a constant hidden behind Euler＇s constant γ, the constant θ is the perfect combination of μ and γ, and the new formula describes the real number relation between π and e, which is different from the imaginary number relation of Euler＇s formula π=1/2eθ. The typical applications of the new formula can be seen in the transformation between = and e, and μ and γ. In this paper presents a computing formula for μ, which can be used to quickly calculate the Eulez＇s constant γ. Many commonly used formulas can be greatly simplified if we use eθ/2 instead of √2π.

关 键 词：欧拉常数γ 圆周率Π 自然对数的底e 常数μ 常数θ 公式π=1/2eθ 

分 类 号：O21[理学—概率论与数理统计]