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

Feng  Qi; Christian Berg

doi:10.1007/s00009-013-0272-2

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

Feng Qi, Christian Berg

Institut for Matematiske Fag

24 Citationer (Scopus)

Abstract

In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αeβ/t, α, β > 0, and the trigamma function ψ
(t) to be completely monotonic on (0,∞).
While proving the complete onotonicity, the authors discover some properties related to the first order modified Bessel function of the first kind I1, including inequalities, monotonicity, unimodality, and convexity.

Originalsprog	Engelsk
Tidsskrift	Mediterranean Journal of Mathematics
Vol/bind	10
Udgave nummer	4
Sider (fra-til)	1685–1696
ISSN	1660-5446
DOI	https://doi.org/10.1007/s00009-013-0272-2
Status	Udgivet - nov. 2013

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10.1007/s00009-013-0272-2

Citationsformater

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N2 - In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αeβ/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.

AB - In the paper, the authors find necessary and sufficient conditions for a difference between the exponential function αeβ/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.

U2 - 10.1007/s00009-013-0272-2

DO - 10.1007/s00009-013-0272-2

M3 - Journal article

SN - 1660-5446

VL - 10

SP - 1685

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JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 4

ER -

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

Abstract

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