Complete monotonicity of a function involving the p-psi function and alternative proofs

  • Authors

    • Valmir Krasniqi Department of Mathematics, University of Prishtina, Prishtine 10000, Republic of Kosova
    • Feng Qi Department of Mathematics, College of Science, Tianjin Polytechnic University Tianjin City, 300160, China
    2014-08-03
    https://doi.org/10.14419/gjma.v2i3.3096

  • Abstract

    In the paper, the authors prove that the function $x^\alpha\big[\ln\frac{px}{x+p+1}-\psi_p(x)\big]$ is completely monotonic on $(0,\infty)$ if and only if $\alpha \le 1$, where $p\in\mathbb{N}$ and $\psi_p(x)$ is the $p$-analogue of the classical psi function $\psi(x)$.

    Keywords: completely monotonic function; necessary and sufficient condition; p-gamma function; p-psi function; Inequality

    MSC: Primary 33D05; Secondary 26A48, 33B15, 33E50

     

    Author Biography

    • Feng Qi, Department of Mathematics, College of Science, Tianjin Polytechnic University Tianjin City, 300160, China

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  • How to Cite

    Krasniqi, V., & Qi, F. (2014). Complete monotonicity of a function involving the p-psi function and alternative proofs. Global Journal of Mathematical Analysis, 2(3), 204-208. https://doi.org/10.14419/gjma.v2i3.3096

    Received date: 2014-06-30

    Accepted date: 2014-07-26

    Published date: 2014-08-03