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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.21 No.2

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COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2014, v.21 no.2, pp.141-145
https://doi.org/10.7468/jksmeb.2014.21.2.141
Qi, Feng
Zhang, Xiao-Jing
Qi,, F. , & Zhang,, X. (2014). COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 21(2), 141-145, https://doi.org/10.7468/jksmeb.2014.21.2.141

Abstract

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function <TEX>$e^{1/t}$</TEX> and the trigamma function <TEX>${\psi}^{\prime}(t)$</TEX> on (0, <TEX>${\infty}$</TEX>).

keywords
complete monotonicity, completely monotonic function, integral representation, difference, exponential function, trigamma function, inequality, modifid Bessel function of the fist kind

Reference

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M. Abramowitz & I.A. Stegun (Eds). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Applied Mathematics Series 55.

2.

B.-N. Guo & F. Qi. (2012). A completely monotonic function involving the tri-gamma function and with degree one. Appl. Math. Comput., 218(19), 9890-9897. 10.1016/j.amc.2012.03.075.

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B.-N. Guo & F. Qi. (2013). Refinements of lower bounds for polygamma functions. Proc. Amer. Math. Soc., 141(3), 1007-1015. 10.1090/S0002-9939-2012-11387-5.

4.

F. Qi. (2013). Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions. Classical Analysis and ODEs, 1, 21.

5.

F. Qi & C. Berg. (2013). Complete monotonicity of a difference between the exponential and trigamma functions and properties related to a modified Bessel function. Mediterr. J. Math., 10(4), 1685-1696. 10.1007/s00009-013-0272-2.

6.

F. Qi & S.-H. Wang. (2012). Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions. Classical Analysis and ODEs, 1, 6.

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F. Qi & X.-J. Zhang. (2013). Complete monotonicity of a difference between the exponential and trigamma functions. Classical Analysis and ODEs, 1, 4.

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D.V. Widder. The Laplace Transform.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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