Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function |
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| Authors: | Feng Qi Christian Berg |
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| Institution: | 1. College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, China
2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, Copenhagen, DK-2100, Denmark
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| 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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