Euler常数的数学表示及其应用

Mathematical Expressions of Euler's Constant and Its Applications

数列an=(1+12+13+…+1n)-ln n收敛于Eu ler常数γ,且γ有多种数学表达形式.我们通过格玛函数Γ(x)的两种不同表达方式建立Eu ler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）-lnn ,converges to Euler＇s constant γ, and Euler＇s constant γ has many mathematical forms. We construct three different mathematical forms of Euler＇s constant T 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 Eulcr＇s constant γ.