Research And Improvement Of Convergence To Euler-Mascheroni Constant Sequence

The Euler-Mascheroni constants play a key role in many areas of mathe-matics and science in general.Up until now,many researchers are devoted to the theory of concerning the Euler-Mascheroni constant and establish faster se-quences to converge to Euler-Mascheroni constant.In this paper,we improve the sequences,which converge to Euler-Mascheroni constant and get some in-equality estimates.What's more,on the basis of constructing the new sequences,we obtain asymptotic expansion for the psi function and the Euler-Mascheroni constant.In chapter 1,we introduce the background significance and research status of the faster sequences and the definition of Euler-Mascheroni constant,psi function as well as relevant knowledge are given.In chapter 2,we introduce some new faster sequences to converge to Euler-Mascheroni constant,and by the numerical computations to prove the superiority of our new convergent sequences over DeTemple's sequence,Lu's sequence and Chen's sequence.In chapter 3,By researching the new sequences,we obtain asymptotic expansion for the psi function and the Euler-Mascheroni constant,and we get some responding inequalities.