Mediterranean Journal of Mathematics

, Volume 10, Issue 4, pp 1685–1696 | Cite as

Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function

  • Feng QiEmail author
  • Christian Berg


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.

Mathematics Subject Classification (2010)

Primary 26A48 33C10 Secondary 26A51 33B10 33B15 44A10 


Complete monotonicity difference trigamma function exponential function necessary and sufficient condition inequality monotonicity convexity unimodality modified Bessel function 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.College of MathematicsInner Mongolia University for NationalitiesTongliao CityChina
  2. 2.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark

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