A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw's double inequality

In the article, the sufficient and necessary conditions such that a class of functions which involve the psi function @j and the ratio @C(x+t)/@C(x+s) are logarithmically completely monotonic are established, the best bounds for the ratio @C(x+t)/@C(x+s) are given, and some comparisons with known results are carried out, where s and t are two real numbers and x>-min{s,t}.

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