Sharp bounds for psi function

In this paper, we present the greatest value a ∈ (1/15, ∞) and the least value b   ∈ (4/15, ∞) such that the double inequality L(x,a)<ψ(x+1) 0, where L(x,a)=190a2+2log(x2+x+3a+13)+45a290a2+2log(x2+x+15a−145a) and ψ(x) is the classical psi function.