Research article

Completely monotonic degree of a function involving trigamma and tetragamma functions

  • Received: 19 November 2019 Accepted: 25 March 2020 Published: 01 April 2020
  • MSC : Primary: 33B15; Secondary: 26A12, 26A48, 26A51, 42A85, 44A10, 44A35

  • Let $\psi(x)$ be the digamma function. In the paper, the author reviews backgrounds and motivations to compute complete monotonic degree of the function $\Psi(x) = [\psi'(x)]^2+\psi''(x)$ with respect to $x\in(0, \infty)$, confirms that completely monotonic degree of the function $\Psi(x)$ is $4$, finds a relation between strongly completely monotonic functions and completely monotonic degrees, provides a proof for the relation between strongly completely monotonic functions and completely monotonic degrees, proves a property of logarithmically concave functions, and poses two open problems on lower bound for convolution of logarithmically concave functions and on completely monotonic degree of a function involving $\Psi(x)$.

    Citation: Feng Qi. Completely monotonic degree of a function involving trigamma and tetragamma functions[J]. AIMS Mathematics, 2020, 5(4): 3391-3407. doi: 10.3934/math.2020219

    Related Papers:

  • Let $\psi(x)$ be the digamma function. In the paper, the author reviews backgrounds and motivations to compute complete monotonic degree of the function $\Psi(x) = [\psi'(x)]^2+\psi''(x)$ with respect to $x\in(0, \infty)$, confirms that completely monotonic degree of the function $\Psi(x)$ is $4$, finds a relation between strongly completely monotonic functions and completely monotonic degrees, provides a proof for the relation between strongly completely monotonic functions and completely monotonic degrees, proves a property of logarithmically concave functions, and poses two open problems on lower bound for convolution of logarithmically concave functions and on completely monotonic degree of a function involving $\Psi(x)$.


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