For the investigation of a mathematical expression of Euler’s constant γ

we have further optimized an estimation of a weak boundary of Stieltjes’s constant γk=limn→∞ S(k)N=∑Nn=1lnknn-1k+1lnk+1(N+1)(k=0

1

2

…).After that

with regard to Euler’s constant γ=limx→0+(∑∞n=11n1+x-1x)

we expand the right function of this equation to a power series of x and discuss its consistent convergence detailedly.Final

we have gotten a nwe mathematical expression on Euler constant γ by construting a function: g(x)=∑∞n=1(-1)n-1n...