Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions

  • Authors

    • Feng Qi Department of Mathematics, College of Science, Tianjin Polytechnic University Tianjin City, 300389, China
    • Shu-Hong Wang College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, China
    2014-06-23
    https://doi.org/10.14419/gjma.v2i3.2919

  • Abstract

    In the paper, the authors verify the complete monotonicity of the difference $e^{1/t}-\psi'(t)$ on $(0,\infty)$, compute the completely monotonic degree and establish integral representations of the remainder of the Laurent series expansion of $e^{1/z}$, and derive an inequality which gives a lower bound for the first order modified Bessel function of the first kind. These results show us some new properties and relations of the exponential, trigamma, the first kind modified Bessel functions and the hypergeometric series.

    Keywords: property; connection; completely monotonic function; completely monotonic degree; integral representation; difference;exponential function; trigamma function; hypergeometric series; inequality; modified Bessel function.

    Author Biography

    • Feng Qi, Department of Mathematics, College of Science, Tianjin Polytechnic University Tianjin City, 300389, China

  • References

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  • How to Cite

    Qi, F., & Wang, S.-H. (2014). Complete monotonicity, completely monotonic degree, integral representations, and an inequality related to the exponential, trigamma, and modified Bessel functions. Global Journal of Mathematical Analysis, 2(3), 91-97. https://doi.org/10.14419/gjma.v2i3.2919

    Received date: 2014-05-25

    Accepted date: 2014-06-21

    Published date: 2014-06-23