On the log-concavity of the fractional integral of the sine function

JOURNAL OF APPROXIMATION THEORY

卷:210

Article

Koumandos, Stamatis¹ 

[1] Univ Cyprus, Dept Math & Stat, POB 20537, CY-1678 Nicosia, Cyprus

关键词: Logarithmically concave functions;    Fractional integrals;    Trigonometric integrals;    Lommel functions;    Monotonicity properties;    Turan type inequalities;   

DOI  :  10.1016/j.jat.2016.06.004

来源: Elsevier

【 摘 要 】

We prove that the function F-lambda(x) := integral(x)(0) (x-t)(lambda) sin t dt is logarithmically concave on (0, infinity) if and only lambda >= 2. As a consequence, a Turk type inequality for certain Lommel functions of the first kind is obtained. Furthermore, some monotonicity properties of functions involving the remainders of the Taylor series expansion of the functions sin x and cos x are given. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free