Abstract
In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αe β/t, α, β > 0, and the trigamma function ψ′(t) to be completely monotonic on (0, ∞). While proving the complete monotonicity, the authors discover some properties related to the first order modified Bessel function of the first kind I 1, including inequalities, monotonicity, unimodality, and convexity.
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Qi, F., Berg, C. Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function. Mediterr. J. Math. 10, 1685–1696 (2013). https://doi.org/10.1007/s00009-013-0272-2
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DOI: https://doi.org/10.1007/s00009-013-0272-2