DECREASING MONOTONICITY OF TWO RATIOS DEFINED BY THREE OR FOUR POLYGAMMA FUNCTIONS

Feng Qi (1, 2, 3)

1 Henan Polytechnic University
2 Tianjin Polytechnic University
3 Inner Mongolia University for Nationalities

In the paper, by virtue of convolution theorem for the Laplace transforms, by three monotonicity rules for the ratios of two definite integrals, of two Laplace transforms, and of two functions, and by other analytic techniques, the author presents decreasing monotonicity of two ratios defined by three or four polygamma functions. These results confirm guesses posed by the author.

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 MONOTONICITY OF TWO RATIOS DEFINED BY THREE OR FOUR POLYGAMMA FUNCTIONS. 2020. ⟨hal-02998414v1⟩