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COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS

Feng Qi|Xiao-Jing Zhang
한국수학교육학회|2014.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제21권 제2호|pp. 141-145

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참고문헌

키워드

inequalitydifferencecompletely monotonic functionexponential functioncomplete monotonicitymodified Bessel function of the first kindintegral repre- sentationtrigamma function
주제분류수학

초록

In the paper, by directly verifying an inequality which gives a lowerbound for the first order modified Bessel function of the first kind, the authors supplya new proof for the complete monotonicity of a difference between the exponentialfunction e^(1/t) and the trigamma function ψ'(t) on (0, ∞).

Abstract

In the paper, by directly verifying an inequality which gives a lowerbound for the first order modified Bessel function of the first kind, the authors supplya new proof for the complete monotonicity of a difference between the exponentialfunction e^(1/t) and the trigamma function ψ'(t) on (0, ∞).

참고문헌 (8)

  1. M. Abramowitz, "Handbook of Mathematical Functions with For-mulas, Graphs, and Mathematical Tables" (1970), National Bureau of Standards
  2. B.-N. Guo, "A completely monotonic function involving the tri-gamma function and with degree one", Appl. Math. Comput, 218(19), pp.9890~9897 (2012)
  3. B.-N. Guo, "Refinements of lower bounds for polygamma functions", Proc. Amer. Math. Soc, 141(3), pp.1007~1015 (2013)
  4. "Properties of modiffed Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions"[URL]
  5. F. Qi, "Complete monotonicity of a difference between the ex-ponential and trigamma functions and properties related to a modi¯ed Bessel function", Mediterr. J. Math, 10, pp.1685~1696 (2013)
  6. "Complete monotonicity, completely monotonic de-gree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions"[URL]
  7. "Complete monotonicity of a difference between the exponential and trigamma functions"[URL]
  8. D.V. Widder, "The Laplace Transform" (1946), Princeton University Press

관련 논문AI추천

Some completely monotonic functions involving the gamma and polygamma functionsAi-Jun Li, Chao-Ping Chen대한수학회 · 대한수학회지2008 · 제45권 제1호TWO NEW PROOFS OF THE COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE PSI FUNCTIONBai-Ni Guo, Feng Qi대한수학회 · 대한수학회보2010 · 제47권 제1호Some inequalities and absolute monotonicity for modified Bessel functions of the first kindBai-Ni Guo, Feng Qi대한수학회 · 대한수학회논문집2016 · 제31권 제2호COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE TRI- AND TETRA-GAMMA FUNCTIONSQ. Feng장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제2호Inequalities and complete monotonicity for the gamma and related functions최준상, Chao-Ping Chen대한수학회 · 대한수학회논문집2019 · 제34권 제4호NEW COMPLETE MONOTONICITY PROPERTIES OF THE GAMMA FUNCTIONBatir장전수학회 · Advanced Studies in Contemporary Mathematics2009 · 제19권 제2호

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