Complete monotonicity properties of a function involving the polygamma function

2018/06/27 by Nantomah, Kwara
#26A48 #26D07 #33B15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1807.05257

Abstract

In this paper, we study completete monotonicity properties of the function f_a,k(x)=ψ^(k)(x+a) - ψ^(k)(x) - \fracak!x^k+1, where a∈(0,1) and k∈ ℕ₀. Specifically, we consider the cases for k∈ \ 2n: n∈ ℕ₀ \ and k∈ \ 2n+1: n∈ ℕ₀ \. Subsequently, we deduce some inequalities involving the polygamma functions.

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