Expressions And Inequalities With Euler-mascheroni Constant

Euler-Mascheroni constant is an important mathematical constant in num-ber theory.In this paper we obtained a modified consequence toward Euler con-stant,and an inequality is built to estimate the convergence speed.Also we studied an analogue of e?,obtaining an asymptotic series,and an inequality with best constants is obtained.This article is organised as follows.In the first part of this article,we construct a consequence and give a proof that it converges to Euler-Mascheroni constant.Then using the method by De-temple we get the estimation of this consequence,which is determined by the parameter s in the modified consequence.In the second part of this article,a product form of Pn=(?)is construct-ed to study the constant of e?.And using Digamma function,an asymptotic series is obtained.Also,we build an inequality with best constants to estimate Pn with r = 2,a = 1.