In this paper our aim is to deduce some complete monotonicity properties and
functional inequalities for the Bickley function. The key tools in our proofs
are the classical integral inequalities, like Chebyshev, H\"older-Rogers,
Cauchy-Schwarz, Carlson and Gr\"uss inequalities, as well as the monotone form
of l'Hospital's rule. Moreover, we prove the complete monotonicity of a
determinant function of which entries involve the Bickley function.Comment: 10 page
