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Some inequalities for the trigamma function in terms of the digamma function

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  • Qi, Feng
  • Mortici, Cristinel

Abstract

In the paper, the authors establish three kinds of inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The method in the paper utilizes some facts from the asymptotic theory and is a natural way to solve problems for approximating some quantities for large values of the variable.

Suggested Citation

  • Qi, Feng & Mortici, Cristinel, 2015. "Some inequalities for the trigamma function in terms of the digamma function," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 502-511.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:502-511
    DOI: 10.1016/j.amc.2015.09.039
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    References listed on IDEAS

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    1. Qi, Feng & Mortici, Cristinel, 2015. "Some best approximation formulas and inequalities for the Wallis ratio," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 363-368.
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    Cited by:

    1. Ladislav Matejíčka, 2019. "A Solution to Qi’s Conjecture on a Double Inequality for a Function Involving the Tri- and Tetra-Gamma Functions," Mathematics, MDPI, vol. 7(11), pages 1-14, November.

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