Article ID Journal Published Year Pages File Type
4593358 Journal of Number Theory 2016 12 Pages PDF
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)∼ln⁡x+(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
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