We prove that the function F λ ( x ) : = ź 0 x ( x - t ) λ sin t d t is logarithmically concave on ( 0 , ∞ ) if and only if λ ź 2 . As a consequence, a Turan 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.
['Stamatis Koumandos']
On the log-concavity of the fractional integral of the sine function