Decreasing properties of two ratios defined by three and four polygamma functions

Feng Qi (1, 2)

1 Henan Polytechnic University
2 Tianjin Polytechnic University

In the paper, by virtue of convolution theorem for the Laplace transforms, with the aid of three monotonicity rules for the ratios of two functions, of two definite integrals, and of two Laplace transforms, in terms of the majorization, and in the light of other analytic techniques, the author presents decreasing properties of two ratios defined by three and four polygamma functions.

Mots clés: decreasing monotonicity; ratio; polygamma function; exponential function; majorization; inequality; convolution theorem for the Laplace transform; monotonicity rule for the ratio of two Laplace transforms; monotonicity rule for the ratio of two definite integrals; monotonicity rule for the ratio of two functions

Domaines: Analyse classique [math.CA]

Feng Qi. Decreasing properties of two ratios defined by three and four polygamma functions. Comptes Rendus. Mathématique, 2022, 360, pp.89--101. ⟨10.5802/crmath.296⟩. ⟨hal-02998414v2⟩