Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593358 | Journal of Number Theory | 2016 | 12 Pages |
Abstract
Let r≠0r≠0 and s≠0s≠0 be two given real numbers. We give a recursive relation for determining the coefficients aj(r,s)aj(r,s) such thatψ(x+1)∼lnx+(1−1r)1x+1sln(1+∑j=1∞aj(r,s)xj),x→∞, where ψ denotes the psi function. As a consequence, we obtain asymptotic expansion for the Euler–Mascheroni constant. Furthermore, we present new inequalities for the psi function. As a consequence, we obtain the higher order estimate for the Euler–Mascheroni constant.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Chao-Ping Chen,