摘要
数列an=(1+12+13+…+1n)-lnn收敛于Euler常数γ,且γ有多种数学表达形式。本文通过格玛函数Γ(x)的两种不同表达方式建立Euler常数γ的三个不同的数学表达式,并由此来计算有关非正常积分、级数的和以及无穷乘积的值等。
The series of number： an=（1＋1/2＋1/3＋…＋1/n）-1nn converges to Euler＇s constant γ, and Euler＇sconstant γ has many mathematical forms. We shall construct three different mathematical forms of Euler＇s constant γ by two different mathematical forms of Gamma＇s function, and calculate the improper integral, the sums of some numeral series, the infinite product and so on by Euler＇s constant γ.
